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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285741550

Chapter 10.4, Problem 47E

Textbook Problem

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Find the exact length of the polar curve.

**47.** *r* = *θ*^{2}, 0 ≤ *θ* ≤ 2*π*

To determine

The exact length of the polar curve,

**Formula used:**

The exact length of the polar curve is,

**Calculation:**

The given polar curve is

Differentiate the polar equation

Substitute *r* and

Let *t* with respect to

Substitute 0 for

Substitute

Then, the limits are

Calculus: Early Transcendentals

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Finding Higher-Order Derivatives In Exercises 93100, find the higher-order derivative. GivenDerivativef(x)=9x3f...

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Sketch the graph of an example of a function f that satisfies all of the given conditions. limx3f(x)=,limxf(x)=...

Single Variable Calculus: Early Transcendentals, Volume I

Evaluate the double integral by first identifying it as the volume of a solid. 10. R(2x+1)dA,R={(x,y)|0x2,0y4}

Multivariable Calculus

You are the governor of the state and must decide which of four metropolitan police departments will win an awa...

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Two scores, X and Y, are recorded for each of n = 5 participants. For these scores, find the value of each expr...

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

1520 Identify the curve by finding a Cartesian equation for the curve. r=4sec

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For a population with =40and =11 , find the a-score for each of the following X values. (Note: You probably wil...

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Find the limit. 25. limx0cos(x+sinx)

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In Exercises 18, determine whether the equation defines y as a linear function of x. If so, write it in the for...

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The Pew Forum on Religion and Public Life reported on Dec. 9, 2009, that in a survey of 2003 American adults, 2...

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Critical Thinking Josh and Kendra each calculated a 90% confidence interval for the difference of means using a...

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By any method, determine all possible real solutions of each equation in Exercises 1330. Check your answers by ...

Finite Mathematics

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State the property of equality that justifies writing x+4=6 for 6=x+4.

Intermediate Algebra

Solve the following word problems. Round dollars to the nearest cent and percent to the nearest tenth of a perc...

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

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In Problems 35-40, (a) graph each function with a graphing utility; (b) classify each function as a...

Mathematical Applications for the Management, Life, and Social Sciences

In Exercises 55 and 56, P is a true statement, while Q and R are false statements. Classify each of the followi...

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Area of a Region In Exercises 55-58, use the integration capabilities of a graphing utility to approximate the ...

Calculus: Early Transcendental Functions (MindTap Course List)

For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 2?

Single Variable Calculus: Early Transcendentals

Using Intercepts and Symmetry to Sketch a Graph in Exercises 9-14, find any intercepts and test for symmetry. T...

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For each expression below, write an equivalent algebraic expression that involves x only. (For Problems 89 thro...

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Show that in=im for all integers n, where nm(mod4).

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True or False: In many applications of definite integrals, the integral is used to compute the total amount of ...

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

Sometimes, Always, or Never:
If {an} is increasing and bounded above, then {an} converges.

Study Guide for Stewart's Multivariable Calculus, 8th

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Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 9 to 16, factor each trinomial product. 12a2+31a+20

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Rectangular-to-Cylindrical ConversionIn Exercises 914, convert the point from rectangular coordinates to cylind...

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Think About It Describe the relationship between the rate of change of y and the rate of change of x in each ex...

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List the following signed numbers in order of increasing value starting with the smallest number. a. +17, -1, +...

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Practice Graph each inequality. yx

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In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ...

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Table 1.7 shows data for eight cordless telephones (Consumer Reports, November 2012). The Overall Score, a meas...

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Psychology journals and medical journals tend to use different formats for citations. Locate a report in a medi...

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Consider the study described in the previous exercise. Explain why taking two separate random samples has the s...

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Suppose bot and top are positive integers with bottop. Consider the array a[bot],a[bot+1],,a[top] . a. How many...

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Reminder Round all answers to two decimal places unless otherwise indicated. Note Some of the formulas below us...

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Marketing Ethics. In the digital age of marketing, special care must be taken to make sure that programmatic ad...

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