(1) log (9)+ log, (4) is equal to: B) 2 A) logo (13) (2) Solve the equation In (1) = 2: e²+1 e²+1 A) 2+1 e2-1 B) C) 1-82 (3) The solutions of e2x + ex-6=0 are: A) x = ln(2), In(3) A) -2 -8 4 (8) √3 x²+9 TT (6) Suppose that x = 3 tan 8, then cos 0 = =: √x²-9 A) √√9-x² B) C) √9+x² A) C) x = 2,-3 D) x = In (2) (4) Assume f is a differentiable function, f x³ f'(x) dx = A) x³ f(x) - fx¹ f(x) dx B)x f(x) + c C) x³ f"(x)-3 f x² f(x) dx (5) Which of the following improper integrals converge: A) x dx B)e-2x dx x dx = B) x = ln(2), In(-3) C) logo (2) (7) According to the method of partial fractions, B) C) -1 B) 4 (9) The derivative of 2 sin (2sin-¹x) In 2 A) √1-x2 2+2e -1 -1x B) C) is: 2sin 1x √1-x² D) D) 2+2e 1-e C) D) 6 √x²+9 3x (x-1)(x-2)(x-3) D)3 D) Diverges In 2 (2sin-1x) In √1+x² = D) x³ f(x)-3 f x² f(x) dx D) In (x) dx (x-1) + B (x-2) + (x-3) the value of B is D) (2 cos-¹x) In 2 √1-x²
(1) log (9)+ log, (4) is equal to: B) 2 A) logo (13) (2) Solve the equation In (1) = 2: e²+1 e²+1 A) 2+1 e2-1 B) C) 1-82 (3) The solutions of e2x + ex-6=0 are: A) x = ln(2), In(3) A) -2 -8 4 (8) √3 x²+9 TT (6) Suppose that x = 3 tan 8, then cos 0 = =: √x²-9 A) √√9-x² B) C) √9+x² A) C) x = 2,-3 D) x = In (2) (4) Assume f is a differentiable function, f x³ f'(x) dx = A) x³ f(x) - fx¹ f(x) dx B)x f(x) + c C) x³ f"(x)-3 f x² f(x) dx (5) Which of the following improper integrals converge: A) x dx B)e-2x dx x dx = B) x = ln(2), In(-3) C) logo (2) (7) According to the method of partial fractions, B) C) -1 B) 4 (9) The derivative of 2 sin (2sin-¹x) In 2 A) √1-x2 2+2e -1 -1x B) C) is: 2sin 1x √1-x² D) D) 2+2e 1-e C) D) 6 √x²+9 3x (x-1)(x-2)(x-3) D)3 D) Diverges In 2 (2sin-1x) In √1+x² = D) x³ f(x)-3 f x² f(x) dx D) In (x) dx (x-1) + B (x-2) + (x-3) the value of B is D) (2 cos-¹x) In 2 √1-x²
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 please solve questionnnn 6
![### Mathematics Multiple Choice Questions
#### (1) Evaluating logarithms:
\[ \log_6 (9) + \log_6 (4) \text{ is equal to:} \]
A) \( \log_6 (13) \)
B) 2
C) \( \log_6 \left(\frac{9}{4} \right) \)
D) 6
#### (2) Solving the logarithmic equation:
\[ \ln \left( \frac{x-1}{x+1} \right) = 2: \]
A) \( \frac{e^2 + 1}{e^2 - 1} \)
B) \( \frac{e^{ \pm 1} + 2}{e^2 - 2} \)
C) \( \frac{2 + 2e}{1 - e^2} \)
D) \( \frac{e^2 + 2}{e^2 - 2} \)
#### (3) Finding solutions to the exponential equation:
\[ e^x + e^{-x} = 6 \]
A) \( x = \ln(2), \ln(3) \)
B) \( x = \ln(2), \ln(-3) \)
C) \( x = 2, -3 \)
D) \( x = \ln(2) \)
#### (4) Working with differentiable functions:
\[ \int x^3 f'(x) \, dx = \]
A) \( x^3 f(x) - \frac{1}{4} x^4 f(x) \, dx \)
B) \( \frac{1}{4} x^4 f(x) + c \)
C) \( x^3 f^{''}(x) - 3 \int x^2 f(x) \, dx \)
D) \( x^3 f(x) - 3 \int x^2 f'(x) \, dx \)
#### (5) Convergence of improper integrals:
Which of the following improper integrals converge?
A) \( \int_0^\infty x^8 \, dx \)
B) \( \int_{-\infty}^0 e^{-2x} \, dx \)
C) \( \int_3^\infty \frac{\ln(x)}{x}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5231f5b4-e859-48c1-839f-bbb3459ab86b%2Ffd91b367-6721-4387-9d11-a5a3f3fbfd16%2F9asrawh_processed.png&w=3840&q=75)
Transcribed Image Text:### Mathematics Multiple Choice Questions
#### (1) Evaluating logarithms:
\[ \log_6 (9) + \log_6 (4) \text{ is equal to:} \]
A) \( \log_6 (13) \)
B) 2
C) \( \log_6 \left(\frac{9}{4} \right) \)
D) 6
#### (2) Solving the logarithmic equation:
\[ \ln \left( \frac{x-1}{x+1} \right) = 2: \]
A) \( \frac{e^2 + 1}{e^2 - 1} \)
B) \( \frac{e^{ \pm 1} + 2}{e^2 - 2} \)
C) \( \frac{2 + 2e}{1 - e^2} \)
D) \( \frac{e^2 + 2}{e^2 - 2} \)
#### (3) Finding solutions to the exponential equation:
\[ e^x + e^{-x} = 6 \]
A) \( x = \ln(2), \ln(3) \)
B) \( x = \ln(2), \ln(-3) \)
C) \( x = 2, -3 \)
D) \( x = \ln(2) \)
#### (4) Working with differentiable functions:
\[ \int x^3 f'(x) \, dx = \]
A) \( x^3 f(x) - \frac{1}{4} x^4 f(x) \, dx \)
B) \( \frac{1}{4} x^4 f(x) + c \)
C) \( x^3 f^{''}(x) - 3 \int x^2 f(x) \, dx \)
D) \( x^3 f(x) - 3 \int x^2 f'(x) \, dx \)
#### (5) Convergence of improper integrals:
Which of the following improper integrals converge?
A) \( \int_0^\infty x^8 \, dx \)
B) \( \int_{-\infty}^0 e^{-2x} \, dx \)
C) \( \int_3^\infty \frac{\ln(x)}{x}
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