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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calculusssss please solve question 7
![**Integral Convergence and Divergence Problems**
6. Given that the improper integral \( \int_{1}^{\infty} x^p - 2 \, dx \) converges, then "p" should be:
a. \( p < 1 \)
b. \( p <-1 \)
c. \( p > 1 \)
d. \( p > -1 \)
7. One of the following sequences is a divergent sequence:
a. \( \left( \frac{2^n}{n!} \right) \)
b. \( (-1)^n \frac{3n^4 + 2n}{n^5 + 7} \)
c. \( \{(-1)^n e^{-3n} \} \)
d. \( \{(-1)^n \frac{n^2 + 4n}{5n + n^2} \} \)
8. The sum of \( \sum_{n=0}^{\infty} \frac{(-1)^n 2 n}{n!} \)
a. \( e^{-π^2} \)
b. \( -e^{π^2} \)
c. \( cos π \)
d. \( -cos π \)
9. For the series \( \sum ( -1 ) \frac { n^2 + 3 } { n + 10 } \), one of the statements is true:
a. Converges by Integral Test
b. Diverges by Divergence Test
c. Converges by Alternating Series Test
d. Diverges by Root Test
10. The interval of convergence of the Power series: \( \sum ( -1 ) ^ n \frac { ( x - 4 ) ^ n } { n } \) is:
a. \( ( 3, 5 ) \)
b. \( [ 3, 5 ) \)
c. \( [ 3, 5 ] \)
d. \( ( 3, 5 ] \)
11. The series \( \sum_{m=1}^{∞} \left( \frac { 1 } { 3 } \right) ^ n \), has sum equal to:
a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F651a6648-31bf-414e-9733-041ee5de2545%2F277db38f-c838-4cdc-8219-d3bbbb07ff60%2Fvo6ddjy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Integral Convergence and Divergence Problems**
6. Given that the improper integral \( \int_{1}^{\infty} x^p - 2 \, dx \) converges, then "p" should be:
a. \( p < 1 \)
b. \( p <-1 \)
c. \( p > 1 \)
d. \( p > -1 \)
7. One of the following sequences is a divergent sequence:
a. \( \left( \frac{2^n}{n!} \right) \)
b. \( (-1)^n \frac{3n^4 + 2n}{n^5 + 7} \)
c. \( \{(-1)^n e^{-3n} \} \)
d. \( \{(-1)^n \frac{n^2 + 4n}{5n + n^2} \} \)
8. The sum of \( \sum_{n=0}^{\infty} \frac{(-1)^n 2 n}{n!} \)
a. \( e^{-π^2} \)
b. \( -e^{π^2} \)
c. \( cos π \)
d. \( -cos π \)
9. For the series \( \sum ( -1 ) \frac { n^2 + 3 } { n + 10 } \), one of the statements is true:
a. Converges by Integral Test
b. Diverges by Divergence Test
c. Converges by Alternating Series Test
d. Diverges by Root Test
10. The interval of convergence of the Power series: \( \sum ( -1 ) ^ n \frac { ( x - 4 ) ^ n } { n } \) is:
a. \( ( 3, 5 ) \)
b. \( [ 3, 5 ) \)
c. \( [ 3, 5 ] \)
d. \( ( 3, 5 ] \)
11. The series \( \sum_{m=1}^{∞} \left( \frac { 1 } { 3 } \right) ^ n \), has sum equal to:
a
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