Calculus

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) | 6th Edition | ISBN: 9780495011699 | Authors: James Stewart
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Author: James Stewart
Publisher: Cengage Learning
ISBN: 9780495011699
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Chapter 3 Problems

Chapter: 3 Problem: 3.3.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate f!x" ! 3x f!x" ! sx sin x 2 " 2 cos x

Chapter: 3 Problem: 3.7.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A particle moves according to a law of motion s=! f !t", t . 0 where t is measured in seconds and s in feet. (a) Find the velocity at time . (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total distance tra

Chapter: 3 Problem: 3.8.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A population of protozoa develops with a constant relative 3. growth rate of 0.7944 per member per day. On day zero the population consists of two members. Find the population size after six days.

Chapter: 3 Problem: 3.4.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Write the composite function in the form . [Identify the 3 inner function and the outer function .] Then find the derivative .

Chapter: 3 Problem: 3.9.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
If V is the volume of a cube with edge length and the cube expands as time passes, find dV!dt in terms of dx!dt

Chapter: 3 Problem: 3.10.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the linearization L!x" of the function at a f !x" ! x a ! %1

Chapter: 3 Problem: 3.1.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Use the given graph to estimate the value of each derivative. f Then sketch the graph of f !

Chapter: 3 Problem: 3.5.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find y by implicit differentiation. (b) Solve the equation explicitly for y and differentiate to get in terms of . (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).

Chapter: 3 Problem: 3.11.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the numerical value of each expression. (a) (b)

Chapter: 3 Problem: 3.2.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of y ! !x 2 " 1"!x 3 " 1" in two ways: by using the Product Rule and by performing the multiplication first. Do your answers agree?

Chapter: 3 Problem: 3.6.1

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Explain why the natural logarithmic function y ! ln x is used much more frequently in calculus than the other logarithmic functions y ! loga x

Chapter: 3 Problem: 3.3.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate f!x" ! sx sin x

Chapter: 3 Problem: 3.7.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A particle moves according to a law of motion s=! f !t", t . 0 where t is measured in seconds and s in feet. (a) Find the velocity at time . (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total distance tra

Chapter: 3 Problem: 3.8.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 60 cells. (a) Find the relative growth rate. (b) Find an expression for the number of cells af

Chapter: 3 Problem: 3.4.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Write the composite function in the form . [Identify the 3 inner function and the outer function .] Then find the derivative .

Chapter: 3 Problem: 3.9.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) If is the area of a circle with radius and the circle expands as time passes, find in terms of . (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of , how fast is the area of the spill increasing when the

Chapter: 3 Problem: 3.10.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the linearization L!x" of the function at a f !x" ! ln x a ! 1

Chapter: 3 Problem: 3.1.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Use the given graph to estimate the value of each derivative. f Then sketch the graph of f !

Chapter: 3 Problem: 3.5.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find y by implicit differentiation. (b) Solve the equation explicitly for y and differentiate to get in terms of . (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).

Chapter: 3 Problem: 3.11.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the numerical value of each expression. (a) (b)

Chapter: 3 Problem: 3.2.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function F!x" ! x ! 3xsx sx in two ways: by using the Quotient Rule and by simplifying first. Show that your answers are equivalent. Which method do you prefer?

Chapter: 3 Problem: 3.6.2

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. f !x" ! ln!x 2 ! 10"

Chapter: 3 Problem: 3.3.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate f!x" ! sin x ! y ! 2 csc x ! 5 cos x 1 2 cot x

Chapter: 3 Problem: 3.7.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A particle moves according to a law of motion s=! f !t", t . 0 where t is measured in seconds and s in feet. (a) Find the velocity at time . (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total distance tra

Chapter: 3 Problem: 3.8.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. (a) Find an expression for the number of bacteria after hours. (b) Find the number of bacteria after 3 hours. (c) Find the rate of growth after 3 hours. (d)

Chapter: 3 Problem: 3.4.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Write the composite function in the form . [Identify the 3 inner function and the outer function .] Then find the derivative .

Chapter: 3 Problem: 3.9.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Each side of a square is increasing at a rate of . At what rate is the area of the square increasing when the area of the square is ?

Chapter: 3 Problem: 3.10.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the linearization L!x" of the function at a f !x" ! cos x a ! &$2

Chapter: 3 Problem: 3.1.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Match the graph of each function in (a)(d) with the graph of its derivative in IIV. Give reasons for your choices.

Chapter: 3 Problem: 3.5.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find y by implicit differentiation. (b) Solve the equation explicitly for y and differentiate to get in terms of . (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).

Chapter: 3 Problem: 3.11.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the numerical value of each expression. (a) (b)

Chapter: 3 Problem: 3.2.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate f!x" ! !x 3 " 2x"ex

Chapter: 3 Problem: 3.6.3

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. f!x" ! sin!ln x

Chapter: 3 Problem: 3.3.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! 2 csc x ! 5 cos x

Chapter: 3 Problem: 3.7.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A particle moves according to a law of motion s=! f !t", t . 0 where t is measured in seconds and s in feet. (a) Find the velocity at time . (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total distance tra

Chapter: 3 Problem: 3.8.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A bacteria culture grows with constant relative growth rate. After 2 hours there are 600 bacteria and after 8 hours the count is 75,000. (a) Find the initial population. (b) Find an expression for the population after t hours. (c) Find the number of cells after 5 hours. (d) Find the rate of growth af

Chapter: 3 Problem: 3.4.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Write the composite function in the form . [Identify the 3 inner function and the outer function .] Then find the derivative .

Chapter: 3 Problem: 3.9.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The length of a rectangle is increasing at a rate of and its width is increasing at a rate of . When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

Chapter: 3 Problem: 3.10.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the linearization L!x" of the function at a f !x" ! x a ! 16

Chapter: 3 Problem: 3.1.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Trace or copy the graph of the given function . (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of below it. 4. 6. 7. 8. 9. 10. 12. Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yea

Chapter: 3 Problem: 3.5.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find y by implicit differentiation. (b) Solve the equation explicitly for y and differentiate to get in terms of . (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).

Chapter: 3 Problem: 3.11.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the numerical value of each expression. (a) (b)

Chapter: 3 Problem: 3.2.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate t!x" ! sx ex

Chapter: 3 Problem: 3.6.4

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. f!x" ! ln!sin2 f!x" ! sin!ln x" x

Chapter: 3 Problem: 3.3.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate t!t" ! t t!t" ! 4 sec t ! tan t 3 cos t

Chapter: 3 Problem: 3.7.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Graphs of the velocity functions of two particles are shown, where is measured in seconds. When is each particle speeding up? When is it slowing down? Explain.

Chapter: 3 Problem: 3.8.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The table gives estimates of the world population, in millions, from 1750 to 2000: (a) Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950. Compare with the actual figures. (b) Use the exponential model and the population figures for

Chapter: 3 Problem: 3.4.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Write the composite function in the form . [Identify the 3 inner function and the outer function .] Then find the derivative .

Chapter: 3 Problem: 3.9.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m3 !min . How fast is the height of the water increasing?

Chapter: 3 Problem: 3.10.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the linear approximation of the function f!x" ! s1 % x at a ! 0 and use it to approximate the numbers s0.9 and s0.99 . Illustrate by graphing f and the tangent line.

Chapter: 3 Problem: 3.1.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Trace or copy the graph of the given function . (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of below it. 4. 6. 7. 8. 9. 10. 12. Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yea

Chapter: 3 Problem: 3.5.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the numerical value of each expression. (a) (b)

Chapter: 3 Problem: 3.2.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! ex x 2

Chapter: 3 Problem: 3.6.5

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. f!x" ! log2!1 # 3x"

Chapter: 3 Problem: 3.3.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate t!t" ! 4 sec t ! tan t

Chapter: 3 Problem: 3.7.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Graphs of the position functions of two particles are shown, where is measured in seconds. When is each particle speeding up? When is it slowing down? Explain.

Chapter: 3 Problem: 3.8.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The table gives the population of the United States, in millions, for the years 19002000. (a) Use the exponential model and the census figures for 1900 and 1910 to predict the population in 2000. Compare with the actual figure and try to explain the discrepancy. (b) Use the exponential model and the

Chapter: 3 Problem: 3.4.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Write the composite function in the form . [Identify the 3 inner function and the outer function .] Then find the derivative .

Chapter: 3 Problem: 3.9.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The radius of a sphere is increasing at a rate of 4 mm!s . How fast is the volume increasing when the diameter is 80 mm?

Chapter: 3 Problem: 3.10.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the linear approximation of the function t!x" ! s 3 1 $ x at a ! 0 and use it to approximate the numbers s 3 a ! 0 0.95 and . Illustrate by graphing g and the tangent line

Chapter: 3 Problem: 3.1.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Trace or copy the graph of the given function . (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of below it. 4. 6. 7. 8. 9. 10. 12. Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yea

Chapter: 3 Problem: 3.5.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the numerical value of each expression. (a) (b)

Chapter: 3 Problem: 3.2.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! e x 1 " x

Chapter: 3 Problem: 3.6.6

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function.

Chapter: 3 Problem: 3.3.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate h!$" ! csc $ ! e !cos u ! cu" $ cot $

Chapter: 3 Problem: 3.7.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The position function of a particle is given by s ! t 3 ! 4.5t 2 ! 7t, t . 0 (a) When does the particle reach a velocity of 5 m#s? (b) When is the acceleration 0? What is the significance of 15. this value of ?

Chapter: 3 Problem: 3.8.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Experiments show that if the chemical reaction N2O5 l 2NO2 $ 1 2O2 takes place at 45+C , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows: % d&N2O5% dt ! 0.0005&N2O5% (a) Find an expression for the concentration N O after t seconds if the initial concentrat

Chapter: 3 Problem: 3.4.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
If y ! x dx!dt ! 5 dy!dt x ! 2 3 " 2x

Chapter: 3 Problem: 3.10.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Verify the given linear approximation at a ! 0 . Then determine the values of x for which the linear approximation is accurate to within 0.1. s tan x # x 3 1 % x # 1 % 1 3 x

Chapter: 3 Problem: 3.1.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Trace or copy the graph of the given function . (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of below it. 4. 6. 7. 8. 9. 10. 12. Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yea

Chapter: 3 Problem: 3.5.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity. sinhx sinh x sin (This shows that is an odd function.)

Chapter: 3 Problem: 3.2.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate t!x" ! 3x ! 1 2x " 1

Chapter: 3 Problem: 3.6.7

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. f!x" ! s x 5 ln x

Chapter: 3 Problem: 3.3.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! e u h!$" ! csc $ ! e !cos u ! cu"

Chapter: 3 Problem: 3.7.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
If a ball is given a push so that it has an initial velocity of down a certain inclined plane, then the distance it has rolled after seconds is . (a) Find the velocity after 2 s. (b) How long does it take for the velocity to reach ?

Chapter: 3 Problem: 3.8.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Bismuth-210 has a half-life of 5.0 days. (a) A sample originally has a mass of 800 mg. Find a formula for the mass remaining after days. (b) Find the mass remaining after 30 days. (c) When is the mass reduced to 1 mg? (d) Sketch the graph of the mass function

Chapter: 3 Problem: 3.4.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
If x dy!dt ! 6 dx!dt y ! 4 2 " y2 ! 25

Chapter: 3 Problem: 3.10.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Verify the given linear approximation at a ! 0 . Then determine the values of x for which the linear approximation is accurate to within 0.1. tan x # x

Chapter: 3 Problem: 3.1.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Trace or copy the graph of the given function . (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of below it. 4. 6. 7. 8. 9. 10. 12. Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yea

Chapter: 3 Problem: 3.5.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity. coshx cosh x si (This shows that is an even function.)

Chapter: 3 Problem: 3.2.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate f!t" ! 2t 4 " t 2

Chapter: 3 Problem: 3.6.8

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function.

Chapter: 3 Problem: 3.3.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! x 2 " tan x

Chapter: 3 Problem: 3.7.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
If a stone is thrown vertically upward from the surface of the moon with a velocity of , its height (in meters) after seconds is . (a) What is the velocity of the stone after 3 s? (b) What is the velocity of the stone after it has risen 25 m?

Chapter: 3 Problem: 3.8.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The half-life of cesium-137 is 30 years. Suppose we have a 100-mg sample. (a) Find the mass that remains after years. (b) How much of the sample remains after 100 years? (c) After how long will only 1 mg remain?

Chapter: 3 Problem: 3.4.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
If z dx!dt ! 2 dy!dt ! 3 dz!dt 2 ! x2 " y2

Chapter: 3 Problem: 3.10.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Verify the given linear approximation at a ! 0 . Then determine the values of x for which the linear approximation is accurate to within 0.1. 1$!1 $ 2x" x # 1 $ x 9. 4 # 1 % 8x

Chapter: 3 Problem: 3.1.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Trace or copy the graph of the given function . (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of below it. 4. 6. 7. 8. 9. 10. 12. Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yea

Chapter: 3 Problem: 3.5.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity. cosh x sinh x ex 9.

Chapter: 3 Problem: 3.2.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate V!x" ! !2x3 " 3"!x4 ! 2x"

Chapter: 3 Problem: 3.6.9

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. f!x" ! sin x ln!5x"

Chapter: 3 Problem: 3.3.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! 1 ! sin x x ! cos x

Chapter: 3 Problem: 3.7.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
If a ball is thrown vertically upward with a velocity of 80 ft#s, then its height after seconds is . (a) What is the maximum height reached by the ball? (b) What is the velocity of the ball when it is 96 ft above the ground on its way up? On its way down?

Chapter: 3 Problem: 3.8.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A sample of tritium-3 decayed to 94.5% of its original amount after a year. (a) What is the half-life of tritium-3? (b) How long would it take the sample to decay to 20% of its original amount?

Chapter: 3 Problem: 3.4.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A particle moves along the curve y ! s1 " x 3 . As it reaches the point "2, 3# , the -coordinate is increasing at a rate of 4 cm!s . How fast is the x-coordinate of the point changing at that instant?

Chapter: 3 Problem: 3.10.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Verify the given linear approximation at a ! 0 . Then determine the values of x for which the linear approximation is accurate to within 0.1. x # 1 $ x

Chapter: 3 Problem: 3.1.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Trace or copy the graph of the given function . (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of below it. 4. 6. 7. 8. 9. 10. 12. Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yea

Chapter: 3 Problem: 3.5.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity. cosh x sinh x ex co

Chapter: 3 Problem: 3.2.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate Y!u" ! !u!2 " u!3 "!u5 ! 2u2 "

Chapter: 3 Problem: 3.6.10

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function.

Chapter: 3 Problem: 3.3.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate f!$" ! sec $ 1 ! sec $

Chapter: 3 Problem: 3.7.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 15 mm and it wants to know how the area of a wafer changes when the side length x changes. Find and explain its meaning in this situation. (b) Show that the rate of change of th

Chapter: 3 Problem: 3.8.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Scientists can determine the age of ancient objects by the method of radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and a

Chapter: 3 Problem: 3.4.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) What quantities are given in the problem? (b) What is the unknown? (c) Draw a picture of the situation for any time t. (d) Write an equation that relates the quantities. (e) Finish solving the problem. A plane flying horizontally at an altitude of 1 mi and a speed of 500 m!h passes directly over

Chapter: 3 Problem: 3.10.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the differential of each function (a) y ! x 2 sin 2x (b) y ! lns1 $ t 2

Chapter: 3 Problem: 3.1.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Trace or copy the graph of the given function . (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of below it. 4. 6. 7. 8. 9. 10. 12. Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yea

Chapter: 3 Problem: 3.5.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity. sinhx y sinh x cosh y cosh x sinh y cos

Chapter: 3 Problem: 3.2.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate F!y" ! ( 1 y2 ! 3 y4 )!y " 5y3 11. "

Chapter: 3 Problem: 3.6.11

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. F!t" ! ln 2 # 1) !2t ! 1" 3 !3t # 1" 4

Chapter: 3 Problem: 3.3.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! 1 " sec x tan x

Chapter: 3 Problem: 3.7.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate when mm and explain its meaning. (b) Show that the rate of change of the volume of a cube with r

Chapter: 3 Problem: 3.8.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A curve passes through the point and has the property that the slope of the curve at every point is twice the -coordinate of . What is the equation of the curve?

Chapter: 3 Problem: 3.4.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) What quantities are given in the problem? (b) What is the unknown? (c) Draw a picture of the situation for any time t. (d) Write an equation that relates the quantities. (e) Finish solving the problem. If a snowball melts so that its surface area decreases at a rate of 1 cm !min, find the rate at

Chapter: 3 Problem: 3.10.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the differential of each function (a) y ! s$!1 $ 2s"(b) y ! e%u y ! s$!1 $ 2s" cos u

Chapter: 3 Problem: 3.1.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Shown is the graph of the population function for yeast cells in a laboratory culture. Use the method of Example 1 to (yeast cells) t (hours) P 0 5 10 15 500 P!t" graph the derivative P!!t What does the graph of tell us about the yeast population?

Chapter: 3 Problem: 3.5.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity. coshx y cosh x cosh y sinh x sinh y sin

Chapter: 3 Problem: 3.2.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate R!t" ! !t " et "(3 ! st )

Chapter: 3 Problem: 3.6.12

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function.

Chapter: 3 Problem: 3.3.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! y ! csc $ !$ ! cot $" sin x x 2

Chapter: 3 Problem: 3.7.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find the average rate of change of the area of a circle with respect to its radius as changes from (i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1 (b) Find the instantaneous rate of change when . (c) Show that the rate of change of the area of a circle with respect to its radius (at any ) is equal to the

Chapter: 3 Problem: 3.8.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is . (a) If the temperature of the turkey is after half an hour, what is the temperature after 45 minutes? (b) When will the turkey have cooled to ?

Chapter: 3 Problem: 3.4.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) What quantities are given in the problem? (b) What is the unknown? (c) Draw a picture of the situation for any time t. (d) Write an equation that relates the quantities. (e) Finish solving the problem. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the

Chapter: 3 Problem: 3.10.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the differential of each function (a) y ! u $ 1 u % 1 (b) y ! !1 $ r 3 " %2

Chapter: 3 Problem: 3.1.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The graph shows how the average age of first marriage of Japanese men has varied in the last half of the 20th century. Sketch the graph of the derivative function M!!t". During which years was the derivative negative?

Chapter: 3 Problem: 3.5.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity. coth2 x 1 c csch2

Chapter: 3 Problem: 3.2.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! x 3 1 ! x 2

Chapter: 3 Problem: 3.6.13

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. t!x" ! ln(xsx " 2 # 1)

Chapter: 3 Problem: 3.3.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! csc $ !$ ! cot $"

Chapter: 3 Problem: 3.7.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm#s. Find the rate at which the area within the circle is increasing after (a) 1 s, (b) 3 s, and (c) 5 s. What can you conclude?

Chapter: 3 Problem: 3.8.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A thermometer is taken from a room where the temperature is C to the outdoors, where the temperature is . After one minute the thermometer reads C. (a) What will the reading on the thermometer be after one more minute? (b) When will the thermometer read C?

Chapter: 3 Problem: 3.4.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) What quantities are given in the problem? (b) What is the unknown? (c) Draw a picture of the situation for any time t. (d) Write an equation that relates the quantities. (e) Finish solving the problem. At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km!h and ship B is saili

Chapter: 3 Problem: 3.10.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the differential of each function . (a) y ! e y ! s1 $ ln z tan &t (b) y ! s1 $ ln z

Chapter: 3 Problem: 3.1.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Make a careful sketch of the graph of and below it sketch the graph f!in the same manner as in Exercises 411. Can you guess a formula for f!!x from its graph?

Chapter: 3 Problem: 3.5.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity.

Chapter: 3 Problem: 3.2.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! x " 1 x 3 " x ! 2

Chapter: 3 Problem: 3.6.14

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function.

Chapter: 3 Problem: 3.3.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate f !x" ! xe sin x tan x x csc x

Chapter: 3 Problem: 3.7.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A spherical balloon is being inflated. Find the rate of increase of the surface area with respect to the radius when is (a) 1 ft, (b) 2 ft, and (c) 3 ft. What conclusion can you make?

Chapter: 3 Problem: 3.8.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
When a cold drink is taken from a refrigerator, its temperature is C. After 25 minutes in a C room its temperature has increased to C. (a) What is the temperature of the drink after 50 minutes? (b) When will its temperature be 15+C?

Chapter: 3 Problem: 3.4.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Two cars start moving from the same point. One travels south at 60 mi!h and the other travels west at 25 mi!h. At what rate is the distance between the cars increasing two hours later?

Chapter: 3 Problem: 3.10.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find the differential dy and (b) evaluate dy for the given values of x and dx. y ! e x ! 0 dx ! 0.1

Chapter: 3 Problem: 3.1.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Make a careful sketch of the graph of and below it sketch the graph f!in the same manner as in Exercises 411. Can you guess a formula for f!!x from its graph?

Chapter: 3 Problem: 3.5.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity.

Chapter: 3 Problem: 3.2.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! t 2 " 2 t 4 ! 3t 2 " 1

Chapter: 3 Problem: 3.6.15

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. f!u" ! ln u 1 ! ln!2u"

Chapter: 3 Problem: 3.3.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! x 2 f !x" ! xe sin x tan x

Chapter: 3 Problem: 3.7.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) The volume of a growing spherical cell is , where the radius is measured in micrometers (1 ,m ). Find the average rate of change of with respect to when changes from (i) 5 to 8 ,m (ii) 5 to 6 ,m (iii) 5 to 5.1 ,m (b) Find the instantaneous rate of change of with respect to when ,m. (c) Show that

Chapter: 3 Problem: 3.8.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A freshly brewed cup of coffee has temperature C in a C room. When its temperature is C, it is cooling at a rate of C per minute. When does this occur?

Chapter: 3 Problem: 3.4.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m!s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Chapter: 3 Problem: 3.10.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find the differential dy and (b) evaluate dy for the given values of x and dx. y ! 1$!x $ 1" x ! 1 dx ! %0.01

Chapter: 3 Problem: 3.1.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Make a careful sketch of the graph of and below it sketch the graph f!in the same manner as in Exercises 411. Can you guess a formula for f!!x from its graph?

Chapter: 3 Problem: 3.5.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity.

Chapter: 3 Problem: 3.2.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! t !t ! 1" 2

Chapter: 3 Problem: 3.6.16

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function.

Chapter: 3 Problem: 3.3.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove that d dx !csc x" ! "csc x cot x

Chapter: 3 Problem: 3.7.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The mass of the part of a metal rod that lies between its left end and a point meters to the right is kg. Find the linear density (see Example 2) when is (a) 1 m, (b) 2 m, and (c) 3 m. Where is the density the highest? The lowest?

Chapter: 3 Problem: 3.8.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The rate of change of atmospheric pressure with respect to altitude is proportional to , provided that the temperature is constant. At C the pressure is kPa at sea level and kPa at m. (a) What is the pressure at an altitude of 3000 m? (b) What is the pressure at the top of Mount McKinley, at an altit

Chapter: 3 Problem: 3.4.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A man starts walking north at 4 ft!s from a point . Five minutes later a woman starts walking south at 5 ft!s from a point 500 ft due east of . At what rate are the people moving apart 15 min after the woman starts walking?

Chapter: 3 Problem: 3.10.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find the differential dy and (b) evaluate dy for the given values of x and dx. y ! tan x x ! &$4 dx ! %0.1

Chapter: 3 Problem: 3.1.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Let f !x" ! x 2(a) Estimate the values of , , , and by using a graphing device to zoom in on the graph of f. (b) Use symmetry to deduce the values of , , and . (c) Use the results from parts (a) and (b) to guess a formula for . (d) Use the definition of a derivative to prove that your guess in part (

Chapter: 3 Problem: 3.5.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity.

Chapter: 3 Problem: 3.2.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! !r 2 ! 2r"er

Chapter: 3 Problem: 3.6.17

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. y ! ln & 2 # x # 5x 2 &

Chapter: 3 Problem: 3.3.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove that d dx !sec x" ! sec x tan x

Chapter: 3 Problem: 3.7.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricellis Law gives the volume of water remaining in the tank after minutes as V ! 5000)1 ! 0 % t % 40 Find the rate at which water is draining from the tank after (a) 5 min, (b) 10 min, (c) 20 min,

Chapter: 3 Problem: 3.8.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) If $1000 is borrowed at 8% interest, find the amounts due at the end of 3 years if the interest is compounded (i) annually, (ii) quarterly, (iii) monthly, (iv) weekly, (v) daily, (vi) hourly, and (viii) continuously (b) Suppose $1000 is borrowed and the interest is compounded continuously. If is

Chapter: 3 Problem: 3.4.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft!s. (a) At what rate is his distance from second base decreasing when he is halfway to first base? (b) At what rate is his distance from third base increasing at the same moment?

Chapter: 3 Problem: 3.10.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) Find the differential dy and (b) evaluate dy for the given values of x and dx. y ! cos x x ! &$3 dx ! 0.05

Chapter: 3 Problem: 3.1.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Letf !x" ! x 2 a) Estimate the values of , , , , and by using a graphing device to zoom in on the graph of f. (b) Use symmetry to deduce the values of , , , and . (c) Use the values from parts (a) and (b) to graph . (d) Guess a formula for . (e) Use the definition of a derivative to prove that your g

Chapter: 3 Problem: 3.5.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity.

Chapter: 3 Problem: 3.2.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! 1 s " kes

Chapter: 3 Problem: 3.6.18

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function.

Chapter: 3 Problem: 3.3.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove that d dx !cot x" ! "csc2 x

Chapter: 3 Problem: 3.7.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The quantity of charge in coulombs (C) that has passed through a point in a wire up to time (measured in seconds) is given by . Find the current when (a) s and (b) s. [See Example 3. The unit of current is an ampere ( A C#s).] At what time is the current lowest?

Chapter: 3 Problem: 3.8.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
(a) If $3000 is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded (i) annually, (ii) semiannually, (iii) monthly, (iv) weekly, (v) daily, and (vi) continuously. (b) If is the amount of the investment at time for the case of continuous compo

Chapter: 3 Problem: 3.4.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function.

Chapter: 3 Problem: 3.9.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
The altitude of a triangle is increasing at a rate of 1 cm!min while the area of the triangle is increasing at a rate of 2 cm !min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is ?

Chapter: 3 Problem: 3.10.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Compute and for the given values of and . Then sketch a diagram like Figure 5 showing the line segments with lengths , , and . y ! 2x % x x ! 2 #x ! %0.4

Chapter: 3 Problem: 3.1.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative.

Chapter: 3 Problem: 3.5.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Find dy#dx by implicit differentiation

Chapter: 3 Problem: 3.11.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Prove the identity.

Chapter: 3 Problem: 3.2.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate y ! " v3 ! 2vsv v

Chapter: 3 Problem: 3.6.19

Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) 6
Differentiate the function. y ! ln!e#x ! xe#x 19. "