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(2) The sequence {(1-2¹), A) converges to e7 n=1 B) converges to e-7 C) converges to -7 TL D) diverges D) Diverges

(2) The sequence {(1-2¹), A) converges to e7 n=1 B) converges to e-7 C) converges to -7 TL D) diverges D) Diverges

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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Question

calculus medium, please solve questionnnn 2

This content will be transcribed for presentation on an educational website to aid students in understanding mathematical series, sequences, integrals, and equations. --- ### 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) Does not exist (DNE) 2. **The sequence** \(\left\{ \left(1 - \frac{7}{n}\right)^n \right\}_{n=1}^{\infty}\): - A) Converges to \(e^7\) - B) Converges to \(e^{-7}\) - C) Converges to \(-7\) - D) Diverges 3. **Evaluate the integral** \(\int_{3}^{\infty} \frac{4}{x^2+9} \, dx\): - A) \(\frac{\pi}{4}\) - B) \(\frac{\pi}{2}\) - C) \(\frac{\pi}{3}\) - D) Diverges 4. **The interval of convergence of the power series** \(\sum_{k=1}^{\infty} \left( \frac{2k}{3^k} \right)^k\) **is**: - A) \([0]\) - B) \(\left(-1, \frac{1}{3}\right)\) - C) \((-3, 3)\) - D) \((-∞, ∞)\) 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. **Evaluate** \(\int \frac{x}{(x+2)^2} \,
Transcribed Image Text:This content will be transcribed for presentation on an educational website to aid students in understanding mathematical series, sequences, integrals, and equations. --- ### 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) Does not exist (DNE) 2. **The sequence** \(\left\{ \left(1 - \frac{7}{n}\right)^n \right\}_{n=1}^{\infty}\): - A) Converges to \(e^7\) - B) Converges to \(e^{-7}\) - C) Converges to \(-7\) - D) Diverges 3. **Evaluate the integral** \(\int_{3}^{\infty} \frac{4}{x^2+9} \, dx\): - A) \(\frac{\pi}{4}\) - B) \(\frac{\pi}{2}\) - C) \(\frac{\pi}{3}\) - D) Diverges 4. **The interval of convergence of the power series** \(\sum_{k=1}^{\infty} \left( \frac{2k}{3^k} \right)^k\) **is**: - A) \([0]\) - B) \(\left(-1, \frac{1}{3}\right)\) - C) \((-3, 3)\) - D) \((-∞, ∞)\) 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. **Evaluate** \(\int \frac{x}{(x+2)^2} \,
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