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Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248

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Section
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248
Chapter 7.5, Problem 25E
Textbook Problem
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In Exercises 1–26, decide whether or not the given integral converges. If the integral converges, compute its value. [HINT: See Quick Examples 1–5.]

0 + 2 x x 2 1 d x

To determine

To calculate: The integral 0+2xx21dx if it converges.

Explanation of Solution

Given information:

The provided integral is:

0+2xx21dx

Formula used:

Improper integral with an infinite limit of integration:

abf(x)dx=limr0a0f(x)dx+limr0+0bf(x)dx

Provide that the limit exists.

If the limit exists, then abf(x)dx converges.

Otherwise, abf(x)dx diverges.

Calculation:

Consider the provided integral is 0+2xx21dx.

Consider the formula:

abf(x)dx=acf(x)dx+cbf(x)dx

Substituting 2xx21 for f(x), 0 for a, + for b and 1 for c in above formula to get,

0+2xx21=012xx21dx+1+2xx21dx

Solving first part of the given integral:

01

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Chapter 7 Solutions

Applied Calculus
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In Execises11-20, find the indicated particular...Ch. 7.6 - Sales Your monthly sales of green tea ice cream...Ch. 7.6 - Profit Your monthly profit on sales of avocado ice...Ch. 7.6 - Newtons Law of Cooling For coffee in a ceramic...Ch. 7.6 - Newtons Law of Cooling For coffee in a paper cup,...Ch. 7.6 - Cooling A bowl of clam chowder at 190F is placed...Ch. 7.6 - Heating Suppose that a pie at 20F is put in an...Ch. 7.6 - Market Saturation You have just introduced a new...Ch. 7.6 - Market Saturation Repeat Exercise 27, assuming...Ch. 7.6 - Determining Demand Nancys Chocolates estimates...Ch. 7.6 - Determining Demand Nancys Chocolates estimates...Ch. 7.6 - Linear Differential Equations Exercises 3136 are...Ch. 7.6 - Linear Differential Equations Exercises 3136 are...Ch. 7.6 - Linear Differential Equations Exercises 3136 are...Ch. 7.6 - Linear Differential Equations Exercises 3136 are...Ch. 7.6 - Linear Differential Equations Exercises 3136 are...Ch. 7.6 - Linear Differential Equations Exercises 3136 are...Ch. 7.6 - Approach to Equilibrium The Extrasoft Toy Co. has...Ch. 7.6 - Approach to Equilibrium Spacely Sprockets has just...Ch. 7.6 - Logistic Equation There are many examples of...Ch. 7.6 - Logistic Equation Using separation of variables...Ch. 7.6 - Exercises 4144 require the use of technology....Ch. 7.6 - Exercises 4144 require the use of technology....Ch. 7.6 - Exercises 4144 require the use of technology....Ch. 7.6 - Exercises 4144 require the use of technology....Ch. 7.6 - What is the difference between a particular...Ch. 7.6 - Why is there always an arbitrary constant in the...Ch. 7.6 - Show by example that a second-order differential...Ch. 7.6 - Find a differential equation that is not...Ch. 7.6 - Find a differential equation whose general...Ch. 7.6 - Explain how, knowing the elasticity of demand as a...Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 11-14, find the area of the given...Ch. 7 - In Exercises 11-14, find the area of the given...Ch. 7 - In Exercises 11-14, find the area of the given...Ch. 7 - In Exercises 11-14, find the area of the given...Ch. 7 - In Exercises15-18, find the average value of the...Ch. 7 - In Exercises15-18, find the average value of the...Ch. 7 - In Exercises15-18, find the average value of the...Ch. 7 - In Exercises15-18, find the average value of the...Ch. 7 - In Exercises 19-22, find the 2-unit moving...Ch. 7 - In Exercises 19-22, find the 2-unit moving...Ch. 7 - In Exercises 19-22, find the 2-unit moving...Ch. 7 - In Exercises 19-22, find the 2-unit moving...Ch. 7 - 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Find the limit. limx3x29x2+2x3

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Sketch the graphs of the equations in Exercises 512. xy=x2+1

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Factoring Completely Factor the expression completely. 111. (a + b)2 (a b)2

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Find the linearization L(x) of the function at n. 2. f(x) = sin x, a = /6

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In Exercises 73-80, find the indicated limits, if they exist. 75. limx3x3+x2+1x3+1

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In Problems 76-82, perform the indicated operations and simplify. x2+6x+9x27x+12x2+4x+3x23x4

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Determine whether the series converges or diverges. 21. n=11+n2+n

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Find for x = 3t2 + 1, y = t6 + 6t5. t4 + 5t3 4t3 + 15t2

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True or False: All the hypotheses for the Mean Value Theorem hold for f(x) = 1 − |x| on [−1, 2].

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3.4 SKILL BUILDING EXERCISES Correlation Coefficient The correlation coefficient r is a measure of how well a r...

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