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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 3.10, Problem 42E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

On page 431 of Physics: Calculus, 2d ed., by Eugene Hecht (Pacific Grove, CA: Brooks/Cole, 2000), in the course of deriving the formula T = 2 π L / g for the period of a pendulum of length L, the author obtains the equation aT = –g sin θ for the tangential acceleration of the bob of the pendulum. He then says, “for small angles, the value of θ in radians is very nearly the value of sin θ; they differ by less than 2% out to about 20°.”

(a) Verify the linear approximation at 0 for the sine function:

sin x ≈ x

(b) Use a graphing device to determine the values of x for which sin x and x differ by less than 2%. Then verify Hecht’s statement by converting from radians to degrees.

(a)

To determine

To verify: The linear approximation to the sine function at x=0

Explanation

Given:

The value f(x)=sinx.

Result used:

The linear approximation of the function at x=a is,f(x)≈f(a)+f′(a)(x−a).

Calculation:

The linearization of the function f(x) at x=0 is computed as follows,

Substitute the value a=0 in f(x)≈f(a)+f′(a)(x−a),

f(x)≈f(0)+f′(0)(x)

The derivative of the function f(x)=sinx is, f′(x)=cosx

(b)

To determine

The values of x for which sinx and x differ by less than 2% and verify that the Hecht’s statement by converting from radians to degrees.

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Chapter 3.10,
Problem 41E
Chapter 3.10,
Problem 43E
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Quadratic Equations Find all real solutions of the quadratic equation. 66. x2 + 5x 6 = 0

Precalculus: Mathematics for Calculus (Standalone Book)

Find the derivative. Simplify where possible. 31. f(x)=tanx

Calculus: Early Transcendentals

You have compiled the following information on each of the graduates voted most likely to succeed by a local hi...

Essentials Of Statistics

Gentile, Lynch, Linder, and Walsh (2004) surveyed over 600 eighth-and ninth-grade students asking about their g...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the integral. 18(2w2w3)dw

Calculus (MindTap Course List)

One sample has SS=36 and a second sample has SS=18 . a. If n=4 for both samples, find each of the sample varian...

Statistics for The Behavioral Sciences (MindTap Course List)

Prove the statement using the , definition of a limit and illustrate with a diagram like Figure 9. 15. limx3(1...

Single Variable Calculus

In Exercises 39-54, simplify the expression. (Assume that x, y, r, s, and t are positive.) 42. 5x6y32x2y7

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Suppose the amount of liquid dispensed by a certain machine is uniformly distributed with lower limit A = 8 oz ...

Probability and Statistics for Engineering and the Sciences

Compute P7,7.

Understanding Basic Statistics

In Exercises 516, evaluate the given quantity. log22

Finite Mathematics

In Problems 100-107, cost, revenue, and profit are in dollars and x is the number of units. 106. Profit A firm ...

Mathematical Applications for the Management, Life, and Social Sciences

For Problems 1-10, answer true or false. The terms 5x2y and 6xy2 are similar terms.

Intermediate Algebra

In Exercises 39 and 40, determine whether each statement is true or false for all sets A and B. 39. (A ∪ B) =...

Mathematical Excursions (MindTap Course List)

Calculate the amount of owner's equity and the two leverage ratios for the following companies. Company Total A...

Contemporary Mathematics for Business & Consumers

Solve each pair of linear equations by addition. If there is one common solution, give the ordered pair of the ...

Elementary Technical Mathematics

Use d=x2-x12+y2-y12 to find the length of CD- as described in Exercise 2. In the coordinate system for Exercise...

Elementary Geometry For College Students, 7e

Evaluating a Sum In Exercises 1924, use the properties of summation and Theorem 4.2 to evaluate the sum. Use th...

Calculus of a Single Variable

For what values of a and b is (2, 2.5) an inflection point of the curve x2y + ax + by = 0? What additional infl...

Single Variable Calculus: Early Transcendentals

Review In Exercises 53-70, determine the convergence or divergence of the series using any appropriate test fro...

Calculus: Early Transcendental Functions (MindTap Course List)

Write each complex number in trigonometric form, once using degrees and once using radians. In each case, begin...

Trigonometry (MindTap Course List)

In the ISBN scheme, write the check digit in the form , where is obtained from the weighting vector .

Elements Of Modern Algebra

True or False: An initial-value problem specifies y(x0) = y0 and y(x1) = y1 in the statement of the problem.

Study Guide for Stewart's Multivariable Calculus, 8th

For f(x) = 10x2, f′(3) = _____. 10 20 30 60

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Graphing Utility In Exercises 1-4, plot the straight line with the equation in the standard viewing window. 3.2...

Finite Mathematics for the Managerial, Life, and Social Sciences

If the larger gear has 30 teeth and smaller gear has 18 then the gear ratio larger to smaller is 5:3. When the ...

Elementary Geometry for College Students

Using Stokess TheoremIn Exercises 716, use Stokess Theorem to evaluate CFdr. In each case, C is oriented counte...

Multivariable Calculus

Characteristics of a Graph In your own words, describe the meaning of amplitude and period.

Calculus (MindTap Course List)

Verifying a Reduction Formula In Exercises 79-82, use integration by parts to verify the reduction formula. (A ...

Calculus

Explain why a researcher might have some ethical reservations about beginning the second baseline phase in an A...

Research Methods for the Behavioral Sciences (MindTap Course List)

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being ...

Statistics for Business & Economics, Revised (MindTap Course List)

Explain how sample size and sample variance influence the outcome of a hypothesis test and why a measure of eff...

Research Methods for the Behavioral Sciences (MindTap Course List)

Solve the following exercises: Use the figure to find the value of the following angles. a. Find 1. b. Find 2...

Mathematics For Machine Technology

Find the horizontal asymptotes, if any, of each rational function. Do not graph the function. f(x)=x2+x22x24

College Algebra (MindTap Course List)

Water permeability of concrete can be measured by letting water flow across the surface and determining the amo...

Introduction To Statistics And Data Analysis

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthor...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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