 3.5.1: Why is it not possible to evaluate lim xS0 sin x x by direct substi...
 3.5.2: How is lim xS0 sin x x used in this section?
 3.5.3: Explain why the Quotient Rule is used to determine the derivative o...
 3.5.4: How can you use the derivatives d dx 1sin x2 = cos x, d dx 1tan x2 ...
 3.5.5: Let f 1x2 = sin x. What is the value of f _1p2?
 3.5.6: Where does the graph of sin x have a horizontal tangent line? Where...
 3.5.7: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.8: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.9: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.10: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.11: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.12: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.13: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.14: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.15: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.16: 716. Trigonometric limits Use Theorem 3.11 to evaluate the followin...
 3.5.17: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.18: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.19: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.20: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.21: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.22: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.23: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.24: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.25: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.26: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.27: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.28: 1728. Calculating derivatives Find dy>dx for the following function...
 3.5.29: 2931. Derivatives of other trigonometric functions Verify the follo...
 3.5.30: 2931. Derivatives of other trigonometric functions Verify the follo...
 3.5.31: 2931. Derivatives of other trigonometric functions Verify the follo...
 3.5.32: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.33: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.34: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.35: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.36: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.37: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.38: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.39: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.40: 3240. Derivatives involving other trigonometric functions Find the ...
 3.5.41: 4148. Secondorder derivatives Find y for the following functions y...
 3.5.42: 4148. Secondorder derivatives Find y for the following functions y...
 3.5.43: 4148. Secondorder derivatives Find y for the following functions y...
 3.5.44: 4148. Secondorder derivatives Find y for the following functions y...
 3.5.45: 4148. Secondorder derivatives Find y for the following functions y...
 3.5.46: 4148. Secondorder derivatives Find y for the following functions y...
 3.5.47: 4148. Secondorder derivatives Find y for the following functions y...
 3.5.48: 4148. Secondorder derivatives Find y for the following functions y...
 3.5.49: Explain why or why not Determine whether the following statements a...
 3.5.50: 5055. Trigonometric limits Evaluate the following limits or state t...
 3.5.51: 5055. Trigonometric limits Evaluate the following limits or state t...
 3.5.52: 5055. Trigonometric limits Evaluate the following limits or state t...
 3.5.53: 5055. Trigonometric limits Evaluate the following limits or state t...
 3.5.54: 5055. Trigonometric limits Evaluate the following limits or state t...
 3.5.55: 5055. Trigonometric limits Evaluate the following limits or state t...
 3.5.56: 5661. Calculating derivatives Find dy>dx for the following function...
 3.5.57: 5661. Calculating derivatives Find dy>dx for the following function...
 3.5.58: 5661. Calculating derivatives Find dy>dx for the following function...
 3.5.59: 5661. Calculating derivatives Find dy>dx for the following function...
 3.5.60: 5661. Calculating derivatives Find dy>dx for the following function...
 3.5.61: 5661. Calculating derivatives Find dy>dx for the following function...
 3.5.62: 6265. Equations of tangent lines a. Find an equation of the line ta...
 3.5.63: 6265. Equations of tangent lines a. Find an equation of the line ta...
 3.5.64: 6265. Equations of tangent lines a. Find an equation of the line ta...
 3.5.65: 6265. Equations of tangent lines a. Find an equation of the line ta...
 3.5.66: Locations of tangent lines a. For what values of x does g1x2 = x  ...
 3.5.67: Locations of horizontal tangent lines For what values of x does f 1...
 3.5.68: Matching Match the graphs of the functions in ad with the graphs of...
 3.5.69: Velocity of an oscillator An object oscillates along a vertical lin...
 3.5.70: Damped sine wave The graph of f 1t2 = ekt sin t with k 7 0 is call...
 3.5.71: A differential equation A differential equation is an equation invo...
 3.5.72: Using identities Use the identity sin 2x = 2 sin x cos x to find d ...
 3.5.73: Proof of lim xS0 cos x _ 1 x _ 0 Use the trigonometric identity cos...
 3.5.74: Another method for proving lim xS0 cos x _ 1 x _ 0 Use the halfang...
 3.5.75: Proof of d dx 1cos x2 _ _sin x Use the definition of the derivative...
 3.5.76: Continuity of a piecewise function Let f 1x2 = c 3 sin x x if x _ 0...
 3.5.77: Continuity of a piecewise function Let g1x2 = c 1  cos x 2x if x _...
 3.5.78: Computing limits with angles in degrees Suppose your graphing calcu...
 3.5.79: Derivatives of sinn x Calculate the following derivatives using the...
 3.5.80: Higherorder derivatives of sin x and cos x Prove that d2n dx2n 1si...
 3.5.81: 8184. Identifying derivatives from limits The following limits equa...
 3.5.82: 8184. Identifying derivatives from limits The following limits equa...
 3.5.83: 8184. Identifying derivatives from limits The following limits equa...
 3.5.84: 8184. Identifying derivatives from limits The following limits equa...
 3.5.85: 8586. Difference quotients Suppose that f is differentiable for all...
 3.5.86: 8586. Difference quotients Suppose that f is differentiable for all...
Solutions for Chapter 3.5: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 3.5
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. Since 86 problems in chapter 3.5 have been answered, more than 54648 students have viewed full stepbystep solutions from this chapter. Chapter 3.5 includes 86 full stepbystep solutions.

Addition property of inequality
If u < v , then u + w < v + w

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Equation
A statement of equality between two expressions.

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Initial value of a function
ƒ 0.

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Pie chart
See Circle graph.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Range (in statistics)
The difference between the greatest and least values in a data set.

Real number line
A horizontal line that represents the set of real numbers.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Series
A finite or infinite sum of terms.

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Variation
See Power function.

Xscl
The scale of the tick marks on the xaxis in a viewing window.