Here is the transcription and explanation for the image, suitable for an educational website: --- ### Mathematics Practice Problems **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 \(\left(1 - \frac{1}{3n}\right)^n\) is: - **A)** converges to \(e^7\) - **B)** converges to \(e^{-7}\) - **C)** converges to \(-7\) - **D)** diverges **3.** \(\int_3^\infty \frac{4}{x^2+9} \, dx\) is: - **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)** \(\left(-\frac{1}{3}, \frac{1}{3}\right)\) - **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.** \(\int \frac{x}{(x+2)^2} \, dx\) is: - **A)** \(\frac{3}{x+3} + \ln|x+
Here is the transcription and explanation for the image, suitable for an educational website: --- ### Mathematics Practice Problems **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 \(\left(1 - \frac{1}{3n}\right)^n\) is: - **A)** converges to \(e^7\) - **B)** converges to \(e^{-7}\) - **C)** converges to \(-7\) - **D)** diverges **3.** \(\int_3^\infty \frac{4}{x^2+9} \, dx\) is: - **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)** \(\left(-\frac{1}{3}, \frac{1}{3}\right)\) - **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.** \(\int \frac{x}{(x+2)^2} \, dx\) is: - **A)** \(\frac{3}{x+3} + \ln|x+
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...
Related questions
Question
calculus medium, please solve questionnnn 6
![Here is the transcription and explanation for the image, suitable for an educational website:
---
### Mathematics Practice Problems
**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 \(\left(1 - \frac{1}{3n}\right)^n\) is:
- **A)** converges to \(e^7\)
- **B)** converges to \(e^{-7}\)
- **C)** converges to \(-7\)
- **D)** diverges
**3.** \(\int_3^\infty \frac{4}{x^2+9} \, dx\) is:
- **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)** \(\left(-\frac{1}{3}, \frac{1}{3}\right)\)
- **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.** \(\int \frac{x}{(x+2)^2} \, dx\) is:
- **A)** \(\frac{3}{x+3} + \ln|x+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5231f5b4-e859-48c1-839f-bbb3459ab86b%2Fe2381820-56e5-442b-b7c9-7c06d33eb2ec%2F5n1f96e_processed.png&w=3840&q=75)
Transcribed Image Text:Here is the transcription and explanation for the image, suitable for an educational website:
---
### Mathematics Practice Problems
**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 \(\left(1 - \frac{1}{3n}\right)^n\) is:
- **A)** converges to \(e^7\)
- **B)** converges to \(e^{-7}\)
- **C)** converges to \(-7\)
- **D)** diverges
**3.** \(\int_3^\infty \frac{4}{x^2+9} \, dx\) is:
- **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)** \(\left(-\frac{1}{3}, \frac{1}{3}\right)\)
- **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.** \(\int \frac{x}{(x+2)^2} \, dx\) is:
- **A)** \(\frac{3}{x+3} + \ln|x+
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning