 3.3.3.1: Differentiate f!x" ! 3x f!x" ! sx sin x 2 " 2 cos x
 3.3.7.1: A particle moves according to a law of motion s=! f !t", t . 0 wher...
 3.3.8.1: A population of protozoa develops with a constant relative 3. growt...
 3.3.4.1: Write the composite function in the form . [Identify the 3 inner fu...
 3.3.9.1: If V is the volume of a cube with edge length and the cube expands ...
 3.3.10.1: Find the linearization L!x" of the function at a f !x" ! x a ! %1
 3.3.1.1: Use the given graph to estimate the value of each derivative. f The...
 3.3.5.1: (a) Find y by implicit differentiation. (b) Solve the equation expl...
 3.3.11.1: Find the numerical value of each expression. (a) (b)
 3.3.2.1: Find the derivative of y ! !x 2 " 1"!x 3 " 1" in two ways: by using...
 3.3.6.1: Explain why the natural logarithmic function y ! ln x is used much ...
 3.3.3.2: Differentiate f!x" ! sx sin x
 3.3.7.2: A particle moves according to a law of motion s=! f !t", t . 0 wher...
 3.3.8.2: A common inhabitant of human intestines is the bacterium Escherichi...
 3.3.4.2: Write the composite function in the form . [Identify the 3 inner fu...
 3.3.9.2: (a) If is the area of a circle with radius and the circle expands a...
 3.3.10.2: Find the linearization L!x" of the function at a f !x" ! ln x a ! 1
 3.3.1.2: Use the given graph to estimate the value of each derivative. f The...
 3.3.5.2: (a) Find y by implicit differentiation. (b) Solve the equation expl...
 3.3.11.2: Find the numerical value of each expression. (a) (b)
 3.3.2.2: Find the derivative of the function F!x" ! x ! 3xsxsx in two ways: ...
 3.3.6.2: Differentiate the function. f !x" ! ln!x 2 ! 10"
 3.3.3.3: Differentiate f!x" ! sin x ! y ! 2 csc x ! 5 cos x 12 cot x
 3.3.7.3: A particle moves according to a law of motion s=! f !t", t . 0 wher...
 3.3.8.3: A bacteria culture initially contains 100 cells and grows at a rate...
 3.3.4.3: Write the composite function in the form . [Identify the 3 inner fu...
 3.3.9.3: Each side of a square is increasing at a rate of . At what rate is ...
 3.3.10.3: Find the linearization L!x" of the function at a f !x" ! cos x a ! &$2
 3.3.1.3: Match the graph of each function in (a)(d) with the graph of its de...
 3.3.5.3: (a) Find y by implicit differentiation. (b) Solve the equation expl...
 3.3.11.3: Find the numerical value of each expression. (a) (b)
 3.3.2.3: Differentiate f!x" ! !x 3 " 2x"ex
 3.3.6.3: Differentiate the function. f!x" ! sin!ln x
 3.3.3.4: Differentiate y ! 2 csc x ! 5 cos x
 3.3.7.4: A particle moves according to a law of motion s=! f !t", t . 0 wher...
 3.3.8.4: A bacteria culture grows with constant relative growth rate. After ...
 3.3.4.4: Write the composite function in the form . [Identify the 3 inner fu...
 3.3.9.4: The length of a rectangle is increasing at a rate of and its width ...
 3.3.10.4: Find the linearization L!x" of the function at a f !x" ! x a ! 16
 3.3.1.4: Trace or copy the graph of the given function . (Assume that the ax...
 3.3.5.4: (a) Find y by implicit differentiation. (b) Solve the equation expl...
 3.3.11.4: Find the numerical value of each expression. (a) (b)
 3.3.2.4: Differentiate t!x" ! sx ex
 3.3.6.4: Differentiate the function. f!x" ! ln!sin2 f!x" ! sin!ln x" x
 3.3.3.5: Differentiate t!t" ! t t!t" ! 4 sec t ! tan t 3 cos t
 3.3.7.5: Graphs of the velocity functions of two particles are shown, where ...
 3.3.8.5: The table gives estimates of the world population, in millions, fro...
 3.3.4.5: Write the composite function in the form . [Identify the 3 inner fu...
 3.3.9.5: A cylindrical tank with radius 5 m is being filled with water at a ...
 3.3.10.5: Find the linear approximation of the function f!x" ! s1 % x at a ! ...
 3.3.1.5: Trace or copy the graph of the given function . (Assume that the ax...
 3.3.5.5: Find dy#dx by implicit differentiation
 3.3.11.5: Find the numerical value of each expression. (a) (b)
 3.3.2.5: Differentiate y ! exx 2
 3.3.6.5: Differentiate the function. f!x" ! log2!1 # 3x"
 3.3.3.6: Differentiate t!t" ! 4 sec t ! tan t
 3.3.7.6: Graphs of the position functions of two particles are shown, where ...
 3.3.8.6: The table gives the population of the United States, in millions, f...
 3.3.4.6: Write the composite function in the form . [Identify the 3 inner fu...
 3.3.9.6: The radius of a sphere is increasing at a rate of 4 mm!s . How fast...
 3.3.10.6: Find the linear approximation of the function t!x" ! s3 1 $ x at a ...
 3.3.1.6: Trace or copy the graph of the given function . (Assume that the ax...
 3.3.5.6: Find dy#dx by implicit differentiation
 3.3.11.6: Find the numerical value of each expression. (a) (b)
 3.3.2.6: Differentiate y ! e x1 " x
 3.3.6.6: Differentiate the function.
 3.3.3.7: Differentiate h!$" ! csc $ ! e !cos u ! cu" $ cot $
 3.3.7.7: The position function of a particle is given by s ! t3 ! 4.5t2 ! 7t...
 3.3.8.7: Experiments show that if the chemical reaction N2O5 l 2NO2 $ 12O2 t...
 3.3.4.7: Find the derivative of the function.
 3.3.9.7: If y ! x dx!dt ! 5 dy!dt x ! 2 3 " 2x
 3.3.10.7: Verify the given linear approximation at a ! 0 . Then determine the...
 3.3.1.7: Trace or copy the graph of the given function . (Assume that the ax...
 3.3.5.7: Find dy#dx by implicit differentiation
 3.3.11.7: Prove the identity. sinhx sinh xsin (This shows that is an odd func...
 3.3.2.7: Differentiate t!x" ! 3x ! 12x " 1
 3.3.6.7: Differentiate the function. f!x" ! s x 5 ln x
 3.3.3.8: Differentiate y ! e u h!$" ! csc $ ! e !cos u ! cu"
 3.3.7.8: If a ball is given a push so that it has an initial velocity of dow...
 3.3.8.8: Bismuth210 has a halflife of 5.0 days. (a) A sample originally ha...
 3.3.4.8: Find the derivative of the function.
 3.3.9.8: If x dy!dt ! 6 dx!dt y ! 4 2 " y2 ! 25
 3.3.10.8: Verify the given linear approximation at a ! 0 . Then determine the...
 3.3.1.8: Trace or copy the graph of the given function . (Assume that the ax...
 3.3.5.8: Find dy#dx by implicit differentiation
 3.3.11.8: Prove the identity. coshx cosh xsi (This shows that is an even func...
 3.3.2.8: Differentiate f!t" ! 2t4 " t2
 3.3.6.8: Differentiate the function.
 3.3.3.9: Differentiate y ! x2 " tan x
 3.3.7.9: If a stone is thrown vertically upward from the surface of the moon...
 3.3.8.9: The halflife of cesium137 is 30 years. Suppose we have a 100mg s...
 3.3.4.9: Find the derivative of the function.
 3.3.9.9: If z dx!dt ! 2 dy!dt ! 3 dz!dt 2 ! x2 " y2
 3.3.10.9: Verify the given linear approximation at a ! 0 . Then determine the...
 3.3.1.9: Trace or copy the graph of the given function . (Assume that the ax...
 3.3.5.9: Find dy#dx by implicit differentiation
 3.3.11.9: Prove the identity. cosh x sinh x ex 9.
 3.3.2.9: Differentiate V!x" ! !2x3 " 3"!x4 ! 2x"
 3.3.6.9: Differentiate the function. f!x" ! sin x ln!5x"
 3.3.3.10: Differentiate y ! 1 ! sin xx ! cos x
 3.3.7.10: If a ball is thrown vertically upward with a velocity of 80 ft#s, t...
 3.3.8.10: A sample of tritium3 decayed to 94.5% of its original amount after...
 3.3.4.10: Find the derivative of the function.
 3.3.9.10: A particle moves along the curve y ! s1 " x 3 . As it reaches the p...
 3.3.10.10: Verify the given linear approximation at a ! 0 . Then determine the...
 3.3.1.10: Trace or copy the graph of the given function . (Assume that the ax...
 3.3.5.10: Find dy#dx by implicit differentiation
 3.3.11.10: Prove the identity. cosh x sinh x exco
 3.3.2.10: Differentiate Y!u" ! !u!2 " u!3"!u5 ! 2u2"
 3.3.6.10: Differentiate the function.
 3.3.3.11: Differentiate f!$" ! sec $1 ! sec $
 3.3.7.11: (a) A company makes computer chips from square wafers of silicon. I...
 3.3.8.11: Scientists can determine the age of ancient objects by the method o...
 3.3.4.11: Find the derivative of the function.
 3.3.9.11: (a) What quantities are given in the problem? (b) What is the unkno...
 3.3.10.11: Find the differential of each function (a) y ! x 2 sin 2x (b) y ! l...
 3.3.1.11: Trace or copy the graph of the given function . (Assume that the ax...
 3.3.5.11: Find dy#dx by implicit differentiation
 3.3.11.11: Prove the identity. sinhx y sinh x cosh y cosh x sinh ycos
 3.3.2.11: Differentiate F!y" ! ( 1y2 ! 3y4 )!y " 5y3 11. "
 3.3.6.11: Differentiate the function. F!t" ! ln 2 # 1) !2t ! 1"3!3t # 1"4
 3.3.3.12: Differentiate y ! 1 " sec xtan x
 3.3.7.12: (a) Sodium chlorate crystals are easy to grow in the shape of cubes...
 3.3.8.12: A curve passes through the point and has the property that the slop...
 3.3.4.12: Find the derivative of the function.
 3.3.9.12: (a) What quantities are given in the problem? (b) What is the unkno...
 3.3.10.12: Find the differential of each function (a) y ! s$!1 $ 2s"(b) y ! e%...
 3.3.1.12: Shown is the graph of the population function for yeast cells in a ...
 3.3.5.12: Find dy#dx by implicit differentiation
 3.3.11.12: Prove the identity. coshx y cosh x cosh y sinh x sinh ysin
 3.3.2.12: Differentiate R!t" ! !t " et"(3 ! st )
 3.3.6.12: Differentiate the function.
 3.3.3.13: Differentiate y ! y ! csc $ !$ ! cot $" sin xx 2
 3.3.7.13: (a) Find the average rate of change of the area of a circle with re...
 3.3.8.13: A roast turkey is taken from an oven when its temperature has reach...
 3.3.4.13: Find the derivative of the function.
 3.3.9.13: (a) What quantities are given in the problem? (b) What is the unkno...
 3.3.10.13: Find the differential of each function (a) y ! u $ 1u % 1 (b) y ! !...
 3.3.1.13: The graph shows how the average age of first marriage of Japanese m...
 3.3.5.13: Find dy#dx by implicit differentiation
 3.3.11.13: Prove the identity. coth2x 1 c csch2
 3.3.2.13: Differentiate y ! x 31 ! x 2
 3.3.6.13: Differentiate the function. t!x" ! ln(xsx " 2 # 1)
 3.3.3.14: Differentiate y ! csc $ !$ ! cot $"
 3.3.7.14: A stone is dropped into a lake, creating a circular ripple that tra...
 3.3.8.14: A thermometer is taken from a room where the temperature is C to th...
 3.3.4.14: Find the derivative of the function.
 3.3.9.14: (a) What quantities are given in the problem? (b) What is the unkno...
 3.3.10.14: Find the differential of each function . (a) y ! e y ! s1 $ ln z ta...
 3.3.1.14: Make a careful sketch of the graph of and below it sketch the graph...
 3.3.5.14: Find dy#dx by implicit differentiation
 3.3.11.14: Prove the identity.
 3.3.2.14: Differentiate y ! x " 1x 3 " x ! 2
 3.3.6.14: Differentiate the function.
 3.3.3.15: Differentiate f !x" ! xe sin x tan x x csc x
 3.3.7.15: A spherical balloon is being inflated. Find the rate of increase of...
 3.3.8.15: When a cold drink is taken from a refrigerator, its temperature is ...
 3.3.4.15: Find the derivative of the function.
 3.3.9.15: Two cars start moving from the same point. One travels south at 60 ...
 3.3.10.15: (a) Find the differential dy and (b) evaluate dy for the given valu...
 3.3.1.15: Make a careful sketch of the graph of and below it sketch the graph...
 3.3.5.15: Find dy#dx by implicit differentiation
 3.3.11.15: Prove the identity.
 3.3.2.15: Differentiate y ! t2 " 2t4 ! 3t2 " 1
 3.3.6.15: Differentiate the function. f!u" ! ln u1 ! ln!2u"
 3.3.3.16: Differentiate y ! x 2 f !x" ! xe sin x tan x
 3.3.7.16: (a) The volume of a growing spherical cell is , where the radius is...
 3.3.8.16: A freshly brewed cup of coffee has temperature C in a C room. When ...
 3.3.4.16: Find the derivative of the function.
 3.3.9.16: A spotlight on the ground shines on a wall 12 m away. If a man 2 m ...
 3.3.10.16: (a) Find the differential dy and (b) evaluate dy for the given valu...
 3.3.1.16: Make a careful sketch of the graph of and below it sketch the graph...
 3.3.5.16: Find dy#dx by implicit differentiation
 3.3.11.16: Prove the identity.
 3.3.2.16: Differentiate y ! t!t ! 1"2
 3.3.6.16: Differentiate the function.
 3.3.3.17: Prove that ddx !csc x" ! "csc x cot x
 3.3.7.17: The mass of the part of a metal rod that lies between its left end ...
 3.3.8.17: The rate of change of atmospheric pressure with respect to altitude...
 3.3.4.17: Find the derivative of the function.
 3.3.9.17: A man starts walking north at 4 ft!s from a point . Five minutes la...
 3.3.10.17: (a) Find the differential dy and (b) evaluate dy for the given valu...
 3.3.1.17: Let f !x" ! x 2(a) Estimate the values of , , , and by using a grap...
 3.3.5.17: Find dy#dx by implicit differentiation
 3.3.11.17: Prove the identity.
 3.3.2.17: Differentiate y ! !r 2 ! 2r"er
 3.3.6.17: Differentiate the function. y ! ln & 2 # x # 5x 2&
 3.3.3.18: Prove that ddx !sec x" ! sec x tan x
 3.3.7.18: If a tank holds 5000 gallons of water, which drains from the bottom...
 3.3.8.18: (a) If $1000 is borrowed at 8% interest, find the amountsdue at the...
 3.3.4.18: Find the derivative of the function.
 3.3.9.18: A baseball diamond is a square with side 90 ft. A batter hits the b...
 3.3.10.18: (a) Find the differential dy and (b) evaluate dy for the given valu...
 3.3.1.18: Letf !x" ! x 2 a) Estimate the values of , , , , andby using a grap...
 3.3.5.18: Find dy#dx by implicit differentiation
 3.3.11.18: Prove the identity.
 3.3.2.18: Differentiate y ! 1s " kes
 3.3.6.18: Differentiate the function.
 3.3.3.19: Prove that ddx !cot x" ! "csc2x
 3.3.7.19: The quantity of charge in coulombs (C) that has passed through a po...
 3.3.8.19: (a) If $3000 is invested at 5% interest, find the value of theinves...
 3.3.4.19: Find the derivative of the function.
 3.3.9.19: The altitude of a triangle is increasing at a rate of 1 cm!min whil...
 3.3.10.19: Compute and for the given values of and . Then sketch a diagram lik...
 3.3.1.19: Find the derivative of the function using the definition of derivat...
 3.3.5.19: Find dy#dx by implicit differentiation
 3.3.11.19: Prove the identity.
 3.3.2.19: Differentiate y ! " v3 ! 2vsvv
 3.3.6.19: Differentiate the function. y ! ln!e#x ! xe#x 19. "
 3.3.3.20: Prove, using the definition of derivative, that if , then f#!x" ! "...
 3.3.7.20: Newtons Law of Gravitation says that the magnitude of the force exe...
 3.3.8.20: (a) How long will it take an investment to double in value if the i...
 3.3.4.20: Find the derivative of the function.
 3.3.9.20: A boat is pulled into a dock by a rope attached to the bow of the b...
 3.3.10.20: Compute and for the given values of and . Then sketch a diagram lik...
 3.3.1.20: Find the derivative of the function using the definition of derivat...
 3.3.5.20: Find dy#dx by implicit differentiation
 3.3.11.20: If tanh x 1213, find the values of the other hyperbolic functions at .
 3.3.2.20: Differentiate y ! " v3 ! 2vsvv
 3.3.6.20: Differentiate the function.y ! $ln!1 ! ex"% 2
 3.3.3.21: Find an equation of the tangent line to the curve at the given poin...
 3.3.7.21: Boyles Law states that when a sample of gas is compressed at a cons...
 3.3.4.21: Find the derivative of the function.
 3.3.9.21: At noon, ship A is 100 km west of ship B. Ship A is sailing south a...
 3.3.10.21: Compute and for the given values of and . Then sketch a diagram lik...
 3.3.1.21: Find the derivative of the function using the definition of derivat...
 3.3.5.21: If f !x" ! x f!1" ! 2 f "!1" 2 $ f !x"%3 ! 10 and f!1" ! 2 f "!1"
 3.3.11.21: If cosh x x 0 5 and x 0 , find the values of the other hyperbolic f...
 3.3.2.21: Differentiate f!t" ! 2t2 " st
 3.3.6.21: Differentiate the function. y ! 2x log10sx
 3.3.3.22: Find an equation of the tangent line to the curve at the given poin...
 3.3.7.22: If, in Example 4, one molecule of the product C is formed from one ...
 3.3.4.22: Find the derivative of the function.
 3.3.9.22: A particle is moving along the curve . As the particle passes throu...
 3.3.10.22: Compute and for the given values of and . Then sketch a diagram lik...
 3.3.1.22: Find the derivative of the function using the definition of derivat...
 3.3.5.22: If f!1" ! 2 f "!1" find t"!0"
 3.3.11.22: (a) Use the graphs of , , and in Figures 13 todraw the graphs of , ...
 3.3.2.22: Differentiate t!t" ! t ! stt1%3
 3.3.6.22: Differentiate the function. y ! log2!e#x y ! 2x log10sx cos $x"
 3.3.3.23: Find an equation of the tangent line to the curve at the given poin...
 3.3.7.23: In Example 6 we considered a bacteria population that doubles every...
 3.3.4.23: Find the derivative of the function.
 3.3.9.23: Water is leaking out of an inverted conical tank at a rate of 10,00...
 3.3.10.23: Use a linear approximation (or differentials) to estimate the given...
 3.3.1.23: Find the derivative of the function using the definition of derivat...
 3.3.5.23: Regard y as the independent variable x and as the dependent variabl...
 3.3.11.23: Use the definitions of the hyperbolic functions to find each of the...
 3.3.2.23: Differentiate f!x" ! AB " Cex
 3.3.6.23: Find y" and y+ y ! x 2 ln!2x
 3.3.3.24: Find an equation of the tangent line to the curve at the given poin...
 3.3.7.24: The number of yeast cells in a laboratory culture increases rapidly...
 3.3.4.24: Find the derivative of the function.
 3.3.9.24: A trough is 10 ft long and its ends have the shape of isosceles tri...
 3.3.10.24: Use a linear approximation (or differentials) to estimate the given...
 3.3.1.24: Find the derivative of the function using the definition of derivat...
 3.3.5.24: Regard y as the independent variable x and as the dependent variabl...
 3.3.11.24: Prove the formulas given in Table 1 for the derivatives of the func...
 3.3.2.24: Differentiate f!x" ! 1 ! xexx " ex
 3.3.6.24: Find y" and y+ y ! ln xx 2
 3.3.3.25: (a) Find an equation of the tangent line to the curve at the point ...
 3.3.7.25: The table gives the population of the world in the 20th century. a)...
 3.3.4.25: Find the derivative of the function.
 3.3.9.25: A water trough is 10 m long and a crosssection has the shape of an...
 3.3.10.25: Use a linear approximation (or differentials) to estimate the given...
 3.3.1.25: Find the derivative of the function using the definition of derivat...
 3.3.5.25: Use implicit differentiation to find an equation of the tangent lin...
 3.3.11.25: Give an alternative solution to Example 3 by letting and then using...
 3.3.2.25: Differentiate f!x" ! xx " cx
 3.3.6.25: Find y" and y+ y ! ln(x ! s1 ! x y ! ln!sec x ! tan x" 2 )
 3.3.3.26: (a) Find an equation of the tangent line to the curve at the point ...
 3.3.7.26: The table shows how the average age of first marriage of Japanese w...
 3.3.4.26: Find the derivative of the function.
 3.3.9.26: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow...
 3.3.10.26: Use a linear approximation (or differentials) to estimate the given...
 3.3.1.26: Find the derivative of the function using the definition of derivat...
 3.3.5.26: Use implicit differentiation to find an equation of the tangent lin...
 3.3.11.26: Prove Equation 4.
 3.3.2.26: Differentiate f!x" ! ax " bcx " d
 3.3.6.26: Find y" and y+ y ! ln!sec x ! tan x"
 3.3.6.27: Differentiate f and find the domain of f f!x" ! x1 # ln!x # 1"
 3.3.3.27: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
 3.3.7.27: Refer to the law of laminar flow given in Example 7. Consider a blo...
 3.3.4.27: Find the derivative of the function.
 3.3.9.27: Gravel is being dumped from a conveyor belt at a rate of 30 , and i...
 3.3.10.27: Use a linear approximation (or differentials) to estimate the given...
 3.3.1.27: Find the derivative of the function using the definition of derivat...
 3.3.5.27: Use implicit differentiation to find an equation of the tangent lin...
 3.3.11.27: Prove Equation 5 using (a) the method of Example 3 and (b) Exercise...
 3.3.2.27: Find f%!x" and f '!x". f!x" ! x 4e x
 3.3.6.28: Differentiate f and find the domain of f f!x" ! 11 ! ln x
 3.3.3.28: (a) If , find and . ; (b) Check to see that your answers to part (a...
 3.3.7.28: The frequency of vibrations of a vibrating violin string is given b...
 3.3.4.28: Find the derivative of the function.
 3.3.9.28: A kite 100 ft above the ground moves horizontally at a speed of 8 f...
 3.3.10.28: Use a linear approximation (or differentials) to estimate the given...
 3.3.1.28: Find the derivative of the function using the definition of derivat...
 3.3.5.28: Use implicit differentiation to find an equation of the tangent lin...
 3.3.11.28: For each of the following functions (i) give a definition like thos...
 3.3.2.28: Find f%!x" and f '!x". f!x" ! x 5%2ex
 3.3.6.29: Differentiate f and find the domain of f f!x" ! ln!x f!x" ! ln ln l...
 3.3.3.29: If , find . 30. If f !x" ! sec x, find f '!%%4". 29. H!$" ! $ sin $...
 3.3.7.29: The cost, in dollars, of producing yards of a certain fabric is C#x...
 3.3.4.29: Find the derivative of the function.
 3.3.9.29: Two sides of a triangle are 4 m and 5 m in length and the angle bet...
 3.3.10.29: Explain, in terms of linear approximations or differentials, why th...
 3.3.1.29: Find the derivative of the function using the definition of derivat...
 3.3.5.29: Use implicit differentiation to find an equation of the tangent lin...
 3.3.11.29: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.29: Find f%!x" and f '!x". f!x" ! x 21 " 2x
 3.3.6.30: Differentiate f and find the domain of f f!x" ! ln ln ln x
 3.3.3.30: If f !x" ! sec x, find f '!%%4".
 3.3.7.30: The cost function for production of a commodity is C#x$ ! 339 $ 25x...
 3.3.4.30: Find the derivative of the function.
 3.3.9.30: How fast is the angle between the ladder and the ground changing in...
 3.3.10.30: Explain, in terms of linear approximations or differentials, why th...
 3.3.1.30: (a) Sketch the graph of by starting with the graph of and using the...
 3.3.5.30: Use implicit differentiation to find an equation of the tangent lin...
 3.3.11.30: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.30: Find f%!x" and f '!x".x" ! x3 " ex
 3.3.6.31: If , find .32. If f!x" ! ln!1 ! e , find f "!0". 2x
 3.3.3.31: (a) Use the Quotient Rule to differentiate the function f!x" ! tan ...
 3.3.7.31: If p#x is the total value of the production when there are workers ...
 3.3.4.31: Find the derivative of the function.
 3.3.9.31: Boyles Law states that when a sample of gas is compressed at a cons...
 3.3.10.31: Explain, in terms of linear approximations or differentials, why th...
 3.3.1.31: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
 3.3.5.31: (a) The curve with equation y 2 ! 5x 4 # x 2 is called a kampyle of...
 3.3.11.31: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.31: Find an equation of the tangent line to the given curve at the spec...
 3.3.6.32: If f!x" ! ln!1 ! e , find f "!0".
 3.3.3.32: Suppose f !%%3" ! 4 and f #!%%3" ! "2 and let andt!x" ! f!x" sin x ...
 3.3.7.32: If denotes the reaction of the body to some stimulus of strength , ...
 3.3.4.32: Find the derivative of the function.
 3.3.9.32: When air expands adiabatically (without gaining or losing heat), it...
 3.3.10.32: Let f!x" ! !x % 1"2 t!x" ! e%2x and h!x" ! 1 $ ln!1 % 2x (a) Find t...
 3.3.1.32: (a(a) If , find .; (b) Check to see that your answer to part (a) is...
 3.3.5.32: (a) The curve with equation y 2 ! x 3 ! 3x 2 is called the Tschirnh...
 3.3.11.32: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.32: Find an equation of the tangent line to the given curve at the spec...
 3.3.6.33: Find an equation of the tangent line to the curve at the given poin...
 3.3.3.33: For what values of does the graph of f!x" ! x ! 2 s 2 sin x have a ...
 3.3.7.33: The gas law for an ideal gas at absolute temperature (in kelvins), ...
 3.3.4.33: Find the derivative of the function.
 3.3.9.33: If two resistors with resistances and are connected in parallel, as...
 3.3.10.33: The edge of a cube was found to be 30 cm with a possible error in m...
 3.3.1.33: The unemployment rate varies with time. The table (from the Bureau ...
 3.3.5.33: Find y+ by implicit differentiation
 3.3.11.33: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.33: Find equations of the tangent line and normal line to the given cur...
 3.3.6.34: Find an equation of the tangent line to the curve at the given poin...
 3.3.3.34: Find the points on the curve y ! !cos x"%!2 ! sin x" at whichthe ta...
 3.3.7.34: In a fish farm, a population of fish is introduced into a pond and ...
 3.3.4.34: Find the derivative of the function.
 3.3.9.34: Brain weight as a function of body weight in fish has been modeled ...
 3.3.10.34: The radius of a circular disk is given as 24 cm with a maximum erro...
 3.3.1.34: Let be the percentage of Americans under the age of 18 at time . Th...
 3.3.5.34: Find y+ by implicit differentiation
 3.3.11.34: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.34: Find equations of the tangent line and normal line to the given cur...
 3.3.6.35: If , find . Check that your answer is reasonable by comparing the g...
 3.3.3.35: A mass on a spring vibrates horizontally on a smooth level surface ...
 3.3.7.35: n the study of ecosystems, predatorprey models are often used to s...
 3.3.4.35: Find the derivative of the function.
 3.3.9.35: Two sides of a triangle have lengths 12 m and 15 m. The angle betwe...
 3.3.10.35: he circumference of a sphere was measured to be 84 cm with a possib...
 3.3.1.35: The graph of is given. State, with reasons, the numbers at which is...
 3.3.5.35: Find y+ by implicit differentiation
 3.3.11.35: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.35: (a) The curve y ! 1%!1 " x2" is called a witch of Maria Agnesi. Fin...
 3.3.6.36: Find equations of the tangent lines to the curve y ! !ln x"#x at th...
 3.3.3.36: An elastic band is hung on a hook and a mass is hung on the lower e...
 3.3.4.36: Find the derivative of the function.
 3.3.9.36: Two carts, A and B, are connected by a rope 39 ft long that passes ...
 3.3.10.36: Use differentials to estimate the amount of paint needed to apply a...
 3.3.1.36: The graph of is given. State, with reasons, the numbers at which is...
 3.3.5.36: Find y+ by implicit differentiation
 3.3.11.36: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.36: (a) The curve is y ! x%!1 " x 2 36. " called a serpentine. Find an ...
 3.3.6.37: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.37: A ladder 10 ft long rests against a vertical wall. Let be the angle...
 3.3.4.37: Find the derivative of the function.
 3.3.9.37: A television camera is positioned 4000 ft from the base of a rocket...
 3.3.10.37: (a) Use differentials to find a formula for the approximate volume ...
 3.3.1.37: The graph of is given. State, with reasons, the numbers at which is...
 3.3.5.37: Fanciful shapes can be created by using the implicit plotting capab...
 3.3.11.37: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.37: (a) If f !x" ! e f %!x" x%x 3 , find . ; (b) Check to see that your...
 3.3.6.38: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.38: An object with weight is dragged along a horizontal plane by a forc...
 3.3.4.38: Find the derivative of the function.
 3.3.9.38: A lighthouse is located on a small island 3 km away from the neares...
 3.3.10.38: One side of a right triangle is known to be 20 cm long and the oppo...
 3.3.1.38: The graph of is given. State, with reasons, the numbers at which is...
 3.3.5.38: (a) The curve with equation 2y 3 ! y 2 # y 5 ! x 4 # 2x 3 ! x 2 has...
 3.3.11.38: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.38: f !x" ! e f %!x" x %x 3
 3.3.6.39: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.39: Find the limit. limxl0sin 3xx
 3.3.4.39: Find the derivative of the function.
 3.3.9.39: A plane flies horizontally at an altitude of and passes directly ov...
 3.3.10.39: If a current passes through a resistor with resistance , ( Ohms Law...
 3.3.1.39: Graph the function . Zoom in repeatedly, first toward the point ($1...
 3.3.5.39: Find the points on the lemniscate in Exercise 29 where the tangent ...
 3.3.11.39: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.39: (a) If , find and . ; (b) Check to see that your answers to part (a...
 3.3.6.40: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.40: Find the limit. limxl0sin 4xsin 6x
 3.3.4.40: Find the derivative of the function.
 3.3.9.40: A Ferris wheel with a radius of is rotating at a rate of one revolu...
 3.3.10.40: When blood flows along a blood vessel, the flux (the volume of bloo...
 3.3.1.40: Zoom in toward the points (1, 0), (0, 1), and ($1, 0) on the graph ...
 3.3.5.40: Show by implicit differentiation that the tangent to the ellipse x ...
 3.3.11.40: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.40: (a)If , find and . ; (b) Check to see that your answers to part (a)...
 3.3.6.41: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.41: Find the limit. imtl0tan 6tsin 2t
 3.3.4.41: Find the derivative of the function.
 3.3.9.41: A plane flying with a constant speed of 300 km!h passes over a grou...
 3.3.10.41: Establish the following rules for working with differentials(where ...
 3.3.1.41: The figure shows the graphs of , , and . Identify each curve, and e...
 3.3.5.41: Find an equation of the tangent line to the hyperbola x 2a2 # y 2b2...
 3.3.11.41: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.41: If f !x" ! x f '!1" 2%!1 " x
 3.3.6.42: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.42: Find the limit. lim$l0cos $ " 1sin $
 3.3.4.42: Find the derivative of the function.
 3.3.9.42: Two people start from the same point. One walks east at 3 mi!h and ...
 3.3.10.42: On page 431 of Physics: Calculus, 2d ed., by Eugene Hecht (Pacific ...
 3.3.1.42: The figure shows graphs of , , and . Identify each curve, and expla...
 3.3.5.42: Show that the sum of the x and y intercepts of any tangent line t...
 3.3.11.42: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.42: If t!x" ! x%e !x" x
 3.3.6.43: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.43: Find the limit. lim$l0sin!cos $"sec $
 3.3.4.43: Find the derivative of the function.
 3.3.9.43: A runner sprints around a circular track of radius 100 m at a const...
 3.3.10.43: Suppose that the only information we have about a function is that ...
 3.3.1.43: The figure shows the graphs of three functions. One is the position...
 3.3.5.43: Show, using implicit differentiation, that any tangent line at a po...
 3.3.11.43: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.43: Suppose that f !5" ! 1, , , and f %!5" ! 6 t!5" ! !3. Find the foll...
 3.3.6.44: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.44: Find the limit. limtl0sin2 3tt
 3.3.4.44: Find the derivative of the function.
 3.3.9.44: The minute hand on a watch is 8 mm long and the hour hand is 4 mm l...
 3.3.10.44: Suppose that we dont have a formula for t!x" but we know that t!2" ...
 3.3.1.44: The figure shows the graphs of four functions. One is the position ...
 3.3.5.44: The Power Rule can be proved using implicit differentiation for the...
 3.3.11.44: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.44: Suppose that f!2" ! !3 t!2" !f%!2" ! !2t%!2" ! 7Findh%!2
 3.3.2.45: If f !x" ! e t!0" ! 2 t%!0" ! 5 f%!0" x 45. t!x"
 3.3.6.45: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.45: Find the limit. lim$l0sin $$ ! tan $
 3.3.4.45: Find the derivative of the function.
 3.3.1.45: Use the definition of a derivative to find and . Then graph , , and...
 3.3.5.45: Find the derivative of the function. Simplify where possible. y ! t...
 3.3.11.45: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.46: If h!2" ! 4and h%!2" ! !3
 3.3.6.46: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.46: Find the limit. limxl0sin!x 2"x
 3.3.4.46: Find the derivative of the function.
 3.3.1.46: Use the definition of a derivative to find and . Then graph , , and...
 3.3.5.46: Find the derivative of the function. Simplify where possible. y ! s...
 3.3.11.46: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.47: If and are the functions whose graphs are shown, let u!x" ! f !x"t!...
 3.3.6.47: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.47: Find the limit. lim%l%%41 " tan xsin x " cos x
 3.3.4.47: Find the first and second derivatives of the function h"x# ! sx 2 % 1
 3.3.1.47: If , find , , , and . Graph , , , and on a common screen. Are the g...
 3.3.5.47: Find the derivative of the function. Simplify where possible. y ! s...
 3.3.11.47: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.3.2.48: Let P!x" ! F!x"G!x and Q!x" ! F!x"%G!x", where and are the function...
 3.3.6.48: Use logarithmic differentiation to find the derivative of the funct...
 3.3.3.48: Find the limit. limxl1sin!x " 1"x 2 ! x " 2
 3.3.4.48: Find the first and second derivatives of the function y ! xe cx
 3.3.1.48: (a) The graph of a position function of a car is shown, where s is ...
 3.3.5.48: Find the derivative of the function. Simplify where possible. t!x" ...
 3.3.11.48: The Gateway Arch in St. Louis was designed by Eero Saarinen and was...
 3.3.2.49: If g is a differentiable function, find an expression for the deriv...
 3.3.6.49: Find y" and y ! ln!x 2 ! y 2 y" "
 3.3.3.49: Differentiate each trigonometric identity to obtain a new (or famil...
 3.3.4.49: Find the first and second derivatives of the function y ! e )x sin *x
 3.3.1.49: Let f!x" ! s3 x (a) If , use Equation 2.7.5 to find . (b) Show that...
 3.3.5.49: Find the derivative of the function. Simplify where possible. G!x" ...
 3.3.11.49: If a water wave with length moves with velocity in a body of water ...
 3.3.2.50: If f is a differentiable function, find an expression for the deriv...
 3.3.6.50: Find y" and y ! ln!x 2 ! y 2 y" "
 3.3.3.50: A semicircle with diameter sits on an isosceles triangle PQR to for...
 3.3.4.50: Find the first and second derivatives of the function y ! ee x
 3.3.1.50: (a) If , show that does not exist.(b) If , find .(c) Show that has ...
 3.3.5.50: Find the derivative of the function. Simplify where possible. y ! t...
 3.3.11.50: A flexible cable always hangs in the shape of a catenary y ! c $ a ...
 3.3.2.51: How many tangent lines to the curve ) pass through the point !1, 2"...
 3.3.6.51: Find a formula for f f !x" ! ln!x # 1" !n"!x"
 3.3.3.51: The figure shows a circular arc of length and a chord of length , b...
 3.3.4.51: Find an equation of the tangent line to the curve at the given poin...
 3.3.1.51: Show that the function is not differentiable at 6. Find a formula f...
 3.3.5.51: Find the derivative of the function. Simplify where possible. h!t" ...
 3.3.11.51: A telephone line hangs between two poles 14 m apart in the shape of...
 3.3.2.52: Find equations of the tangent lines to the curve y ! x ! 1x " 1 tha...
 3.3.6.52: Find d9dx 9 !x 8 ln x"
 3.3.4.52: Find an equation of the tangent line to the curve at the given poin...
 3.3.1.52: Where is the greatest integer function not differentiable? Find a f...
 3.3.5.52: Find the derivative of the function. Simplify where possible. F!*" ...
 3.3.11.52: Using principles from physics it can be shown that when a cable is ...
 3.3.2.53: In this exercise we estimate the rate at which the total personal i...
 3.3.6.53: Use the definition of derivative to prove that limxl0ln!1 ! x"x ! 1
 3.3.4.53: Find an equation of the tangent line to the curve at the given poin...
 3.3.1.53: (a) Sketch the graph of the function . (b) For what values of is di...
 3.3.5.53: Find the derivative of the function. Simplify where possible. y ! c...
 3.3.11.53: (a) Show that any function of the form y ! cosh x satisfies the dif...
 3.3.2.54: A manufacturer produces bolts of a fabric with a fixed width. The q...
 3.3.6.54: Show that lim fm for any x  0. n l ( )1 ! xn *n! ex
 3.3.4.54: Find an equation of the tangent line to the curve at the given poin...
 3.3.1.54: The lefthand and righthand derivatives of at are defined by and i...
 3.3.5.54: Find the derivative of the function. Simplify where possible. y ! a...
 3.3.11.54: Evaluate lim . x l + sinh x ex
 3.3.2.55: (a) Use the Product Rule twice to prove that if , , and are differe...
 3.3.4.55: (a) Find an equation of the tangent line to the curve at the point ...
 3.3.1.55: Recall that a function is called even if for all in its domain and ...
 3.3.5.55: Find f"!x"Check that your answer is reasonable by comparingthe grap...
 3.3.11.55: At what point of the curve y ! cosh x does the tangent have slope 1?
 3.3.2.56: (a) If , where and have derivatives of all orders, show that . (b) ...
 3.3.4.56: (a) The curve is called a bulletnose curve. Find an equation of th...
 3.3.1.56: When you turn on a hotwater faucet, the temperature of the water d...
 3.3.5.56: Find f"!x"Check that your answer is reasonable by comparingthe grap...
 3.3.11.56: If x ! ln!sec ( $ tan ( , show that sec ( ! cosh x
 3.3.2.57: Find expressions for the first five derivatives of . Do you see a p...
 3.3.4.57: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
 3.3.1.57: Let be the tangent line to the parabola at the point . The angle of...
 3.3.5.57: Prove the formula for !d#dx"!cos#1x" by the same method asfor !d#dx...
 3.3.11.57: Show that if a " 0 and b " 0 , then there exist numbers and such th...
 3.3.2.58: (a) If t is differentiable, the Reciprocal Rule says that Use the Q...
 3.3.4.58: The function , , arises in applications to frequency modulation (FM...
 3.3.1.58: Where does the normal line to the parabola at the point (1, 0) inte...
 3.3.5.58: (a) One way of defining is to say that and or . Show that, with thi...
 3.3.4.59: Find all points on the graph of the function at which the tangent l...
 3.3.1.59: Draw a diagram to show that there are two tangent lines to the para...
 3.3.5.59: Two curves are orthogonal if their tangent lines are perpendicular ...
 3.3.4.60: Find the coordinates of all points on the curve at which the tange...
 3.3.1.60: a) Find equations of both lines through the point that are tangent ...
 3.3.5.60: Two curves are orthogonal if their tangent lines are perpendicular ...
 3.3.4.61: If F"x# ! f "t"x## where f"#2# ! 8 f$"#2# ! 4 f$"5# ! 3 t"5# ! #2 a...
 3.3.1.61: Use the definition of a derivative to show that if , then . (This p...
 3.3.5.61: Two curves are orthogonal if their tangent lines are perpendicular ...
 3.3.4.62: If h"x# ! s4 % 3f"x# where f "1# ! 7 and f $"1# ! 4 find h$"1#
 3.3.1.62: Find the derivative of each function by calculating the first few d...
 3.3.5.62: Two curves are orthogonal if their tangent lines are perpendicular ...
 3.3.4.63: A table of values for , , , and is given.
 3.3.1.63: Find a seconddegree polynomial P such that P!2"! 5P%!2" ! 3
 3.3.5.63: The equation x 2 # xy ! y 63. 2 ! 3 represents a rotated ellipse, t...
 3.3.4.64: Let f and g be the functions in Exercise 63 (a) If F"x# ! f " f"x##...
 3.3.1.64: The equation is called a differential equation because it involves ...
 3.3.5.64: (a) Where does the normal line to the ellipse at the point intersec...
 3.3.4.65: If f and g are the functions whose graphs are shown, let u"x# ! f "...
 3.3.1.65: Find a cubic function whose graph has horizontal tangents at the po...
 3.3.5.65: Find all points on the curve x 2 y 2 ! xy ! 2 where the slope of th...
 3.3.4.66: If f and g is the function whose graph is shown, let and . Use the ...
 3.3.1.66: Find a parabola with equation that has slope 4 at , slope at , and ...
 3.3.5.66: Find equations of both the tangent lines to the ellipse x !12, 3" 2...
 3.3.4.67: Suppose f is differentiable on ! Let F"x# ! f"ex 67. f ! # and G"x#...
 3.3.1.67: Let f !x" ! #2 ! xx 2 ! 2x " 2if x # 1if x $ 1Is differentiable at ...
 3.3.5.67: (a) Suppose is a onetoone differentiable function and its inverse...
 3.3.4.68: Suppose f s differentiable on ! and ) is a real number Let F"x# ! f...
 3.3.1.68: At what numbers is the following function differentiable? Give a fo...
 3.3.5.68: (a) Show that is onetoone. (b) What is the value of ? (c) Use the...
 3.3.4.69: Let ,r"x# ! f" t"h"x## where h"1# ! 2 t"2# ! 3 ,h$"1# ! 4 ,t$"2# ! ...
 3.3.1.69: (a) For what values of is the function differentiable? Find a formu...
 3.3.5.69: The figure shows a lamp located three units to the right of the ax...
 3.3.4.70: If g is a twice differentiable function and , find in terms of , , ...
 3.3.1.70: Where is the function differentiable? Give a formula for and sketch...
 3.3.4.71: If F"x# ! f "t"x## where f"#2# ! 8 f$"#2# ! 4 f$"5# ! 3 t"5# ! #2 a...
 3.3.1.71: Find the parabola with equation whose tangentline at (1, 1) has equ...
 3.3.4.72: If F"x# ! f "t"x## where f"#2# ! 8 f$"#2# ! 4 f$"5# ! 3 t"5# ! #2 a...
 3.3.1.72: Suppose the curve has a tangent line when with equation and a tange...
 3.3.4.73: Show that the function y ! Ae#x % Bxe#x satisfies the differential ...
 3.3.1.73: For what values of and is the line tangent to the parabola when ?
 3.3.4.74: For what values of does the function y ! erx satisfy the equation y...
 3.3.1.74: Find the value of such that the line is tangent to the curve y ! csx
 3.3.4.75: Find the 50th derivative of y ! cos 2x
 3.3.1.75: Let Find the f !x" ! #x 2mx " bif x # 2if x $ 2 Find the values of ...
 3.3.4.76: Find the 1000th derivative of f"x# ! xe#x
 3.3.1.76: A tangent line is drawn to the hyperbola at a point .(a) Show that ...
 3.3.4.77: The displacement of a particle on a vibrating string is given by th...
 3.3.1.77: Evaluate limxl1x 1000 ! 1x ! 1
 3.3.4.78: If the equation of motion of a particle is given by s ! A cos".t % ...
 3.3.1.78: Draw a diagram showing two perpendicular lines that intersect on th...
 3.3.4.79: A Cepheid variable star is a star whose brightness alternately incr...
 3.3.1.79: If , how many lines through the point are normal lines to the parab...
 3.3.4.80: In Example 4 in Section 1.3 we arrived at a model for the length of...
 3.3.1.80: Sketch the parabolas and . Do you think there is a line that is tan...
 3.3.4.81: The motion of a spring that is subject to a frictional force or a d...
 3.3.4.82: Under certain circumstances a rumor spreads according to the equati...
 3.3.4.83: A particle moves along a straight line with displacement velocity ,...
 3.3.4.84: Air is being pumped into a spherical weather balloon. At any time ,...
 3.3.4.85: The flash unit on a camera operates by storing charge on a capacito...
 3.3.4.86: The table gives the US population from 1790 to 1860. (a) Use a grap...
 3.3.4.87: Computer algebra systems have commands that differentiate functions...
 3.3.4.88: (a) Use a CAS to differentiate the function f "x# ! *x 4 # x % 1x 4...
 3.3.4.89: Use the Chain Rule to prove the following. (a) The derivative of an...
 3.3.4.90: Use the Chain Rule and the Product Rule to give an alternative proo...
 3.3.4.91: (a) If is a positive integer, prove that ddx "sinnx cos nx# ! n sin...
 3.3.4.92: Suppose y ! f "x# is a curve that always lies above the axisand ne...
 3.3.4.93: Use the Chain Rule to show that if is measured in degrees, then dd&...
 3.3.4.94: (a) Writex ) ! sx 2 and use the Chain Rule to show that ddx ) x ) !...
 3.3.4.95: If y ! f "u# and u ! t"x where f and g are twice differentiablefunc...
 3.3.4.96: If y ! f "u# and u ! t"x where f and g possess third derivatives,fi...
Solutions for Chapter 3: Derivatives of Polynomials and Exponential Functions
Full solutions for Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign)  6th Edition
ISBN: 9780495011699
Solutions for Chapter 3: Derivatives of Polynomials and Exponential Functions
Get Full SolutionsSince 608 problems in chapter 3: Derivatives of Polynomials and Exponential Functions have been answered, more than 87261 students have viewed full stepbystep solutions from this chapter. Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780495011699. Chapter 3: Derivatives of Polynomials and Exponential Functions includes 608 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign), edition: 6.

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Control
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

Focal axis
The line through the focus and perpendicular to the directrix of a conic.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Infinite limit
A special case of a limit that does not exist.

Inverse sine function
The function y = sin1 x

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Negative angle
Angle generated by clockwise rotation.

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Transformation
A function that maps real numbers to real numbers.

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.

Zero of a function
A value in the domain of a function that makes the function value zero.