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1. Which of the following statements is/are true? 1. The Laplace transform of f(t) is given by the proper integral L{f(t)} Inverse Laplace Transform also exhibits linearity. II. A) Statement I only B) Statement II only = 2. Find the inverse Laplace transform of F(s): A) 3 sint B) 3et sint A) B) A B + s+1 (s + 1)² B A A) B) 3. What is the partial fraction decomposition of the Laplace transform 4 C +5=1 xe + 1 ex tế xe - e C) Both statements D) None of the choices 4 3 s²2s + 2 ex C) 3sin (t+1) D) + s+ 1 (s + 1)² 4. What is the inverse Laplace transform of the function given in number 3? 1 1 1 1 1 4 C) 1/ex- + zxex. 4 1 D) 0 C) D) None of the choices ? A s+1 Bs + C s² - 1 A and B only + = F(s) = = fe-st f(t)dt. 1 (s + 1)(s² - 1) ?

1. Which of the following statements is/are true? 1. The Laplace transform of f(t) is given by the proper integral L{f(t)} Inverse Laplace Transform also exhibits linearity. II. A) Statement I only B) Statement II only = 2. Find the inverse Laplace transform of F(s): A) 3 sint B) 3et sint A) B) A B + s+1 (s + 1)² B A A) B) 3. What is the partial fraction decomposition of the Laplace transform 4 C +5=1 xe + 1 ex tế xe - e C) Both statements D) None of the choices 4 3 s²2s + 2 ex C) 3sin (t+1) D) + s+ 1 (s + 1)² 4. What is the inverse Laplace transform of the function given in number 3? 1 1 1 1 1 4 C) 1/ex- + zxex. 4 1 D) 0 C) D) None of the choices ? A s+1 Bs + C s² - 1 A and B only + = F(s) = = fe-st f(t)dt. 1 (s + 1)(s² - 1) ?

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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1. Which of the following statements is/are true? I. The Laplace transform of f(t) is given by the proper integral L{f(t)} = fe-st f(t)dt. Inverse Laplace Transform also exhibits linearity. II. A) B) 2. Find the inverse Laplace transform of F(s) A) B) Statement I only Statement II only A) B) 3 sin t 3et sint A) B) A s+1 A + -- 3. What is the partial fraction decomposition of the Laplace transform B C + (s + 1)² s 1 - B xe + -x 4 1 —— = 4 C) D) ex Both statements None of the choices 3 s²2s + 2 C) D) + s+ 1 (s + 1)² 4. What is the inverse Laplace transform of the function given in number 3? 1 1 1 1 70x 4 e-*- -—- xex 2 2 1 1 ex 4 +-xe- 3sin (t+1) None of the choices A s+1 Bs + C C) s²1 D) A and B only ? 1 + C) D) 0 F(s): = 1 Ter 1 (s + 1)(s² - 1) ?
Transcribed Image Text:1. Which of the following statements is/are true? I. The Laplace transform of f(t) is given by the proper integral L{f(t)} = fe-st f(t)dt. Inverse Laplace Transform also exhibits linearity. II. A) B) 2. Find the inverse Laplace transform of F(s) A) B) Statement I only Statement II only A) B) 3 sin t 3et sint A) B) A s+1 A + -- 3. What is the partial fraction decomposition of the Laplace transform B C + (s + 1)² s 1 - B xe + -x 4 1 —— = 4 C) D) ex Both statements None of the choices 3 s²2s + 2 C) D) + s+ 1 (s + 1)² 4. What is the inverse Laplace transform of the function given in number 3? 1 1 1 1 70x 4 e-*- -—- xex 2 2 1 1 ex 4 +-xe- 3sin (t+1) None of the choices A s+1 Bs + C C) s²1 D) A and B only ? 1 + C) D) 0 F(s): = 1 Ter 1 (s + 1)(s² - 1) ?
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