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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)} = fest f(t)dt. Inverse Laplace Transform also exhibits linearity. II. A) B) Statement 1 only Statement 2 only 2. Find the inverse Laplace transform of F(s) A) 3 sin t B) A) B) 3et sin t A s+1 A + B C + (s + 1)² s-1 B = + s+1 (s + 1)² C) Both statements D) None of the choices 3. What is the partial fraction decomposition of the Laplace transform F(s) = 3 s²2s + 2 C) D) C) D) 3sin (t + 1) None of the choices ? A s+1 Bs + C s²1 A and B only + 1 (s + 1)(s² - 1) ?

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)} = fest f(t)dt. Inverse Laplace Transform also exhibits linearity. II. A) B) Statement 1 only Statement 2 only 2. Find the inverse Laplace transform of F(s) A) 3 sin t B) A) B) 3et sin t A s+1 A + B C + (s + 1)² s-1 B = + s+1 (s + 1)² C) Both statements D) None of the choices 3. What is the partial fraction decomposition of the Laplace transform F(s) = 3 s²2s + 2 C) D) C) D) 3sin (t + 1) None of the choices ? A s+1 Bs + C s²1 A and B only + 1 (s + 1)(s² - 1) ?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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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)} Inverse Laplace Transform also exhibits linearity. II. A) B) 2. Find the inverse Laplace transform of F(s) Statement 1 only Statement 2 only A) 3 sin t B) A) B) 3et sin t A) B) A s+1 A + + s+1 (s + 1)² 4 1 4 B C + (s + 1)² S-1 B e 3. What is the partial fraction decomposition of the Laplace transform F(s) = -x -* + xe -x 4 = A) 2 cos 3x - 6 sin 3x B) 2 cos 3x - 2 sin 3x A) Always true B) Always false D) ex s² - 4. What is the inverse Laplace transform of the function given in number 3? 1 1 1 1 2 +=ex 4 2 1 1 2xe C) D) C) D) Both statements None of the choices 3 2s + 2 C) D) 3sin (t + 1) None of the choices C) D) ? A s+1 A and B only C) D) 0 1 + Bs + C s² - 1 2s6 5. What is the inverse Laplace transform of the given function F(s) = s² +9 1 xex + ·ex 4 = 2 2 cos 3x - sin 3x 3 3 cos 3x2 sin 3x Sometimes true None of the choices +∞ fe-stj e-st f(t) dt. 1 (s + 1)(s² - 1) ? 6. The properties of Laplace transform (discussed in class) are all applicable for inverse Laplace transforms. ?
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)} Inverse Laplace Transform also exhibits linearity. II. A) B) 2. Find the inverse Laplace transform of F(s) Statement 1 only Statement 2 only A) 3 sin t B) A) B) 3et sin t A) B) A s+1 A + + s+1 (s + 1)² 4 1 4 B C + (s + 1)² S-1 B e 3. What is the partial fraction decomposition of the Laplace transform F(s) = -x -* + xe -x 4 = A) 2 cos 3x - 6 sin 3x B) 2 cos 3x - 2 sin 3x A) Always true B) Always false D) ex s² - 4. What is the inverse Laplace transform of the function given in number 3? 1 1 1 1 2 +=ex 4 2 1 1 2xe C) D) C) D) Both statements None of the choices 3 2s + 2 C) D) 3sin (t + 1) None of the choices C) D) ? A s+1 A and B only C) D) 0 1 + Bs + C s² - 1 2s6 5. What is the inverse Laplace transform of the given function F(s) = s² +9 1 xex + ·ex 4 = 2 2 cos 3x - sin 3x 3 3 cos 3x2 sin 3x Sometimes true None of the choices +∞ fe-stj e-st f(t) dt. 1 (s + 1)(s² - 1) ? 6. The properties of Laplace transform (discussed in class) are all applicable for inverse Laplace transforms. ?
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