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(7) A formula for the general term starting with n = 1 of: A) {} B) {} C) (-1)" 3") 472 D) 39 - ) - 27 81 64' 256' J 4'16 (-1)n+1 3n 472 *** is:

(7) A formula for the general term starting with n = 1 of: A) {} B) {} C) (-1)" 3") 472 D) 39 - ) - 27 81 64' 256' J 4'16 (-1)n+1 3n 472 *** is:

Calculus: Early Transcendentals
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 7

## Mathematics Practice Questions ### Sequence and Series, Integrals, and Equation Solving 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 \(\left\{(1 - 3)(\frac{7}{n})^3 \right\}_{n=1}^{\infty} \):** - 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 \(\sum_{k=1}^{\infty} \left(\frac{3}{4}\right)^k\) is:** - A) [0] - B) \((-1, \frac{3}{3^{-1}})\) - 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+
Transcribed Image Text:## Mathematics Practice Questions ### Sequence and Series, Integrals, and Equation Solving 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 \(\left\{(1 - 3)(\frac{7}{n})^3 \right\}_{n=1}^{\infty} \):** - 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 \(\sum_{k=1}^{\infty} \left(\frac{3}{4}\right)^k\) is:** - A) [0] - B) \((-1, \frac{3}{3^{-1}})\) - 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+
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