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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calculus medium, please solve questionnnn 1
![Here is the transcribed text from the image for educational use on a website, along with an explanation of any interesting aspects:
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1. The series \(\sum_{k=1}^{\infty} \frac{(-1)^k}{k^4/5}\) is:
- A) conditionally convergent
- B) absolutely convergent
- C) divergent
- D) D.N.E (Does Not Exist)
2. The sequence \(\left \{ (1 - \frac{7}{n})^n \right \}_{n=1}^{\infty}\):
- A) converges to \(e^7\)
- B) converges to \(e^{-7}\)
- C) converges to \(-7\)
- D) diverges
3. \(\int_{3}^{4} \frac{4}{x^2 + 9} \, dx =\)
- A) \(\frac{\pi}{4}\)
- B) \(\frac{\pi}{2}\)
- C) \(\frac{\pi}{3}\)
- D) Diverges
4. The interval of convergence of the power series \(\sum_{k=1}^{\infty} \left( \frac{3}{k} \right)^k\) is:
- A) \([0]\)
- B) \(_{(-1, \frac{1}{3}}\)
- C) \((-3, 3)\)
- D) \((- \infty, \infty)\)
5. The appropriate substitution for \(\int \frac{dx}{ \sqrt{x^2 + 2x + 10} } = \)
- A) \(x + 1 = 3 \tan (\theta)\)
- B) \(x = 10 \sin (\theta)\)
- C) \(x - 1 = 2 \tan (\theta)\)
- D) \(x - 1 = 3 \tan (\theta)\)
6. \(\int \frac{x}{(x + 2)^2} dx =\)
- A) \(\frac{3}{x + 3} + \ln | x + 3 | + c\)
- B) \(\frac{2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5231f5b4-e859-48c1-839f-bbb3459ab86b%2F06362f26-5d00-47ed-84c0-bd954dd0621b%2F2rvtmk_processed.png&w=3840&q=75)
Transcribed Image Text:Here is the transcribed text from the image for educational use on a website, along with an explanation of any interesting aspects:
---
1. The series \(\sum_{k=1}^{\infty} \frac{(-1)^k}{k^4/5}\) is:
- A) conditionally convergent
- B) absolutely convergent
- C) divergent
- D) D.N.E (Does Not Exist)
2. The sequence \(\left \{ (1 - \frac{7}{n})^n \right \}_{n=1}^{\infty}\):
- A) converges to \(e^7\)
- B) converges to \(e^{-7}\)
- C) converges to \(-7\)
- D) diverges
3. \(\int_{3}^{4} \frac{4}{x^2 + 9} \, dx =\)
- A) \(\frac{\pi}{4}\)
- B) \(\frac{\pi}{2}\)
- C) \(\frac{\pi}{3}\)
- D) Diverges
4. The interval of convergence of the power series \(\sum_{k=1}^{\infty} \left( \frac{3}{k} \right)^k\) is:
- A) \([0]\)
- B) \(_{(-1, \frac{1}{3}}\)
- C) \((-3, 3)\)
- D) \((- \infty, \infty)\)
5. The appropriate substitution for \(\int \frac{dx}{ \sqrt{x^2 + 2x + 10} } = \)
- A) \(x + 1 = 3 \tan (\theta)\)
- B) \(x = 10 \sin (\theta)\)
- C) \(x - 1 = 2 \tan (\theta)\)
- D) \(x - 1 = 3 \tan (\theta)\)
6. \(\int \frac{x}{(x + 2)^2} dx =\)
- A) \(\frac{3}{x + 3} + \ln | x + 3 | + c\)
- B) \(\frac{2
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