The function f(r) = is continuous, positive, and decreasing on the interval (7) [3, 00). Use the Integral Test to determine whether the following series is convergent or divergent. Show your work. [You do NOT need to show that f(r) = is continuous, positive, and decreasing on [3, 0).] %3D n2 - 4

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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The function f(r) = is continuous, positive, and decreasing on the interval
(7)
[3, 00). Use the Integral Test to determine whether the following series is convergent or
divergent. Show your work. [You do NOT need to show that f(r) = is continuous,
positive, and decreasing on [3, 0).]
%3D
n2 - 4
Transcribed Image Text:The function f(r) = is continuous, positive, and decreasing on the interval (7) [3, 00). Use the Integral Test to determine whether the following series is convergent or divergent. Show your work. [You do NOT need to show that f(r) = is continuous, positive, and decreasing on [3, 0).] %3D n2 - 4
Expert Solution
Step 1

The given series is n=3nn2-4.

Consider the function fx=xx2-4:

Use the integral test:

3fxdx=3xx2-4dx

Let

 u=x2-4du=2xdxdx=du2xWhen x=3u=5when x=u=

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