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Kvaluate the following integral. If it is convergent, evaluate it. (f the quantity diverges, enter DIVERGES.) Since the integralSelect finite, the serles

Kvaluate the following integral. If it is convergent, evaluate it. (f the quantity diverges, enter DIVERGES.) Since the integralSelect finite, the serles

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

Consider the following series

(View Pictures below)

a) Does the function f(x) = (6) / (x^2+x^3) satisfy the conditions of the Integral Test?

Yes or no

b) Evaluate the following integral. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)

(View Pictures Below)

c) Since the integral (?) finite, the series is (?)

(Answers for the first check box to choose from are: is, is not)

(Answers for the second check box to choose from are: convergent, divergent)

**Evaluate the following integral. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)** \[ \int \frac{2}{x^{3/2}} \, dx \] [ ] **Since the integral is: Select v dx from: Select dx**
Transcribed Image Text:**Evaluate the following integral. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)** \[ \int \frac{2}{x^{3/2}} \, dx \] [ ] **Since the integral is: Select v dx from: Select dx**
**Consider the following series:** \[ \sum_{{n=1}}^{\infty} \frac{6}{{n^2 + n^3}} \] Does the function \( f(x) = \frac{6}{{x^2 + x^3}} \) satisfy the conditions of the Integral Test? - O Yes - O No **Explanation:** This question asks whether the given function \( f(x) \) satisfies the conditions necessary to apply the Integral Test for convergence of the series. The Integral Test requires that \( f(x) \) be positive, continuous, and decreasing for \( x \geq 1 \).
Transcribed Image Text:**Consider the following series:** \[ \sum_{{n=1}}^{\infty} \frac{6}{{n^2 + n^3}} \] Does the function \( f(x) = \frac{6}{{x^2 + x^3}} \) satisfy the conditions of the Integral Test? - O Yes - O No **Explanation:** This question asks whether the given function \( f(x) \) satisfies the conditions necessary to apply the Integral Test for convergence of the series. The Integral Test requires that \( f(x) \) be positive, continuous, and decreasing for \( x \geq 1 \).
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