Let f(n) =an for all positive integers n. What conditions must be met for the Integral Test? Select all that apply. f(x) is decreasing for x ≥ N for some positive integer N. f(x) is positive for x > N for some positive integer N. f(x) is increasing for x > N for some positive integer N. f(x) is continuous for x > N for some positive integer N. Of(x) is concave up for x > N for some positive integer N. f(x) is concave down for x ≥N for some positive integer N.
Let f(n) =an for all positive integers n. What conditions must be met for the Integral Test? Select all that apply. f(x) is decreasing for x ≥ N for some positive integer N. f(x) is positive for x > N for some positive integer N. f(x) is increasing for x > N for some positive integer N. f(x) is continuous for x > N for some positive integer N. Of(x) is concave up for x > N for some positive integer N. f(x) is concave down for x ≥N for some positive integer N.
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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![**Integral Test Conditions for Series Convergence**
Given the function \( f(n) = a_n \) for all positive integers \( n \). To apply the Integral Test for determining the convergence of a series, the following conditions must be met. Select all that apply:
- [✓] \( f(x) \) is decreasing for \( x \ge N \) for some positive integer \( N \).
- [ ] \( f(x) \) is positive for \( x \ge N \) for some positive integer \( N \).
- [✓] \( f(x) \) is increasing for \( x \ge N \) for some positive integer \( N \).
- [ ] \( f(x) \) is continuous for \( x \ge N \) for some positive integer \( N \).
- [ ] \( f(x) \) is concave up for \( x \ge N \) for some positive integer \( N \).
- [ ] \( f(x) \) is concave down for \( x \ge N \) for some positive integer \( N \).
For the Integral Test to be applicable, the function \( f(x) \) must be continuous, positive, and decreasing for all \( x \) greater than or equal to some positive integer \( N \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42d7a143-2adc-420d-86c3-225c6cc98b5a%2F8a9a68b8-dabb-4289-a826-a6d4e20e36e4%2Fku5jjze_processed.png&w=3840&q=75)
Transcribed Image Text:**Integral Test Conditions for Series Convergence**
Given the function \( f(n) = a_n \) for all positive integers \( n \). To apply the Integral Test for determining the convergence of a series, the following conditions must be met. Select all that apply:
- [✓] \( f(x) \) is decreasing for \( x \ge N \) for some positive integer \( N \).
- [ ] \( f(x) \) is positive for \( x \ge N \) for some positive integer \( N \).
- [✓] \( f(x) \) is increasing for \( x \ge N \) for some positive integer \( N \).
- [ ] \( f(x) \) is continuous for \( x \ge N \) for some positive integer \( N \).
- [ ] \( f(x) \) is concave up for \( x \ge N \) for some positive integer \( N \).
- [ ] \( f(x) \) is concave down for \( x \ge N \) for some positive integer \( N \).
For the Integral Test to be applicable, the function \( f(x) \) must be continuous, positive, and decreasing for all \( x \) greater than or equal to some positive integer \( N \).
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