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A) 4 2 (9) The derivative of 2sin-¹x (2sin-1x) In 2 A) √1-x2 B) is: 2sin 1x √1-x² (2sin 1x) In 2 C) √1+x² D) (2cos-¹x) In 2 √1-x²

A) 4 2 (9) The derivative of 2sin-¹x (2sin-1x) In 2 A) √1-x2 B) is: 2sin 1x √1-x² (2sin 1x) In 2 C) √1+x² D) (2cos-¹x) In 2 √1-x²

Advanced Engineering Mathematics
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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please solve questionnnn 9

### Mathematics Exam Questions #### Instructions: Answer the following mathematical questions. Select the correct option from the given choices. Use proper mathematical notations and methods wherever applicable. 1. \( \log_6(9) + \log_6(4) \) is equal to: - A) \( \log_6(13) \) - B) 2 - C) \( \log_6\left(\frac{9}{4}\right) \) - D) 6 2. Solve the equation \(\ln\left(\frac{x-1}{x+1}\right) = 2\): - A) \( \frac{e^2+1}{e^2-1} \) - B) \( \frac{e^{2}+1}{1-e^{2}} \) - C) \( \frac{2+2e}{1-2e} \) - D) \( \frac{2+2e}{2-1} \) 3. The solutions of \(2x+e^x - 6 = 0\) are: - A) \( x = \ln(2), \ln(3) \) - B) \( x = \ln(2), \ln(-3) \) - C) \( x = 2, -3 \) - D) \( x = \ln(2) \) 4. Assume \( f \) is a differentiable function, \(\int x^3 f'(x) \, dx = \): - A) \( x^3 f(x) - \frac{1}{4} x^4 f(x) \, dx \) - B) \( \frac{1}{4} x^4 f(x) + c \) - C) \( x^3 f''(x) - 3 x^2 f(x) \, dx \) - D) \( x^3 f(x) - 3 \int x^2 f(x) \, dx \) 5. Which of the following improper integrals converge: - A) \( \int_0^\infty x^8 \, dx \) - B) \( \int_{-\infty}^\infty e^{-2x} \, dx \) - C) \(
Transcribed Image Text:### Mathematics Exam Questions #### Instructions: Answer the following mathematical questions. Select the correct option from the given choices. Use proper mathematical notations and methods wherever applicable. 1. \( \log_6(9) + \log_6(4) \) is equal to: - A) \( \log_6(13) \) - B) 2 - C) \( \log_6\left(\frac{9}{4}\right) \) - D) 6 2. Solve the equation \(\ln\left(\frac{x-1}{x+1}\right) = 2\): - A) \( \frac{e^2+1}{e^2-1} \) - B) \( \frac{e^{2}+1}{1-e^{2}} \) - C) \( \frac{2+2e}{1-2e} \) - D) \( \frac{2+2e}{2-1} \) 3. The solutions of \(2x+e^x - 6 = 0\) are: - A) \( x = \ln(2), \ln(3) \) - B) \( x = \ln(2), \ln(-3) \) - C) \( x = 2, -3 \) - D) \( x = \ln(2) \) 4. Assume \( f \) is a differentiable function, \(\int x^3 f'(x) \, dx = \): - A) \( x^3 f(x) - \frac{1}{4} x^4 f(x) \, dx \) - B) \( \frac{1}{4} x^4 f(x) + c \) - C) \( x^3 f''(x) - 3 x^2 f(x) \, dx \) - D) \( x^3 f(x) - 3 \int x^2 f(x) \, dx \) 5. Which of the following improper integrals converge: - A) \( \int_0^\infty x^8 \, dx \) - B) \( \int_{-\infty}^\infty e^{-2x} \, dx \) - C) \(
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