2k-1 00 (9) The sum k-13k = A) 312 9/2 C) 2 D) 2/12
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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calculus medium, please solve questionnnn 9
![### Mathematics Multiple Choice Questions
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
2. **The sequence \( \left\{ (1 - \frac{3}{n})^n \right\}_{n=1}^{\infty} \):**
- A) Converges to \( e^7 \)
- B) Converges to \( e^{-7} \)
- C) Converges to \( -7 \)
- D) Diverges
3. **\( \int_{3}^{\infty} \frac{4}{x^2 + 49} \, dx = \)**
- A) \( \frac{\pi}{4} \)
- B) \( \frac{\pi}{2} \)
- C) \( \frac{\pi}{3} \)
- D) Diverges
4. **The interval of convergence of the power series \( \sum_{k=1}^{\infty} \left(\frac{x}{3}\right)^k \) is:**
- A) [0]
- B) \( \left(-1, 1 \right) \)
- C) \((-3, 3)\)
- D) \((-\infty, \infty)\)
5. **The appropriate substitution for \( \int \frac{dx}{\sqrt{x^2 + 2x + 10}} \) is:**
- 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}{x+2} + \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5231f5b4-e859-48c1-839f-bbb3459ab86b%2F49209a66-8a40-4b7d-9987-f920bf11073f%2Fv670zwn_processed.png&w=3840&q=75)
Transcribed Image Text:### Mathematics Multiple Choice Questions
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
2. **The sequence \( \left\{ (1 - \frac{3}{n})^n \right\}_{n=1}^{\infty} \):**
- A) Converges to \( e^7 \)
- B) Converges to \( e^{-7} \)
- C) Converges to \( -7 \)
- D) Diverges
3. **\( \int_{3}^{\infty} \frac{4}{x^2 + 49} \, dx = \)**
- A) \( \frac{\pi}{4} \)
- B) \( \frac{\pi}{2} \)
- C) \( \frac{\pi}{3} \)
- D) Diverges
4. **The interval of convergence of the power series \( \sum_{k=1}^{\infty} \left(\frac{x}{3}\right)^k \) is:**
- A) [0]
- B) \( \left(-1, 1 \right) \)
- C) \((-3, 3)\)
- D) \((-\infty, \infty)\)
5. **The appropriate substitution for \( \int \frac{dx}{\sqrt{x^2 + 2x + 10}} \) is:**
- 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}{x+2} + \
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