(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) (6) Suppose that x = 3 tan 8, then cos 0 = =: √x²-9 A) √√9-x² B) C) √9+x² x dx = 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 = ln(2), In(-3) 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 C) logo (2) B) 4 (9) The derivative of 2 sin (2sin-¹x) In 2 A) √1-x2 2+2e -1 (7) According to the method of partial fractions, C) -1 B) A) -2 -8 4 (8) √3 x²+9 TT -1x C) is: 2sin 1x √1-x² B) 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) (6) Suppose that x = 3 tan 8, then cos 0 = =: √x²-9 A) √√9-x² B) C) √9+x² x dx = 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 = ln(2), In(-3) 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 C) logo (2) B) 4 (9) The derivative of 2 sin (2sin-¹x) In 2 A) √1-x2 2+2e -1 (7) According to the method of partial fractions, C) -1 B) A) -2 -8 4 (8) √3 x²+9 TT -1x C) is: 2sin 1x √1-x² B) 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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Question
calculus please solve questionnnn 4
![**Sample Mathematics Exam Questions for Advanced Calculus**
1. **Evaluate the logarithmic expression:**
\[
\log_6(9) + \log_6(4)
\]
- A) \(\log_6(13)\)
- B) \(2\)
- C) \(\log_6\left(\dfrac{9}{4}\right)\)
- D) \(6\)
2. **Solve the equation:**
\[
\ln\left(\dfrac{x-1}{x+1}\right) = 2
\]
- A) \(\dfrac{e^2+1}{e^2-1}\)
- B) \(\dfrac{e^2+1}{1-e^2}\)
- C) \(\dfrac{2+2e}{1-e}\)
- D) \(\dfrac{e^2-1}{e^2+1}\)
3. **Find the solutions of the quadratic equation:**
\[
e^{2x} + e^x - 6 = 0
\]
- 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, then evaluate the integral:**
\[
\int x^3 f''(x) \, dx
\]
- A) \(x^3 f(x) - \dfrac{1}{4} x^4 f(x) \, dx\)
- B) \(\dfrac{1}{4} x^4 f(x) + c\)
- 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. **Which of the following improper integrals converge?**
- A) \(\int_0^\infty x^{-8} \, dx\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5231f5b4-e859-48c1-839f-bbb3459ab86b%2F677adf98-cc1b-4a1b-a2a4-9a440def0193%2Fae09vth_processed.png&w=3840&q=75)
Transcribed Image Text:**Sample Mathematics Exam Questions for Advanced Calculus**
1. **Evaluate the logarithmic expression:**
\[
\log_6(9) + \log_6(4)
\]
- A) \(\log_6(13)\)
- B) \(2\)
- C) \(\log_6\left(\dfrac{9}{4}\right)\)
- D) \(6\)
2. **Solve the equation:**
\[
\ln\left(\dfrac{x-1}{x+1}\right) = 2
\]
- A) \(\dfrac{e^2+1}{e^2-1}\)
- B) \(\dfrac{e^2+1}{1-e^2}\)
- C) \(\dfrac{2+2e}{1-e}\)
- D) \(\dfrac{e^2-1}{e^2+1}\)
3. **Find the solutions of the quadratic equation:**
\[
e^{2x} + e^x - 6 = 0
\]
- 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, then evaluate the integral:**
\[
\int x^3 f''(x) \, dx
\]
- A) \(x^3 f(x) - \dfrac{1}{4} x^4 f(x) \, dx\)
- B) \(\dfrac{1}{4} x^4 f(x) + c\)
- 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. **Which of the following improper integrals converge?**
- A) \(\int_0^\infty x^{-8} \, dx\
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