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Core Laplace Which of the following represents the Laplace transform L[g] (s) So g(t)e="tdt Off(t)e-st dt at fog(s)est dt So f(t)e="tdt

Core Laplace Which of the following represents the Laplace transform L[g] (s) So g(t)e="tdt Off(t)e-st dt at fog(s)est dt So f(t)e="tdt

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 77E
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Core Laplace Which of the following represents the Laplace transform L[g](s) So g(t)est dt of f(t)e="tdt fog(s)e-st dt What integration technique leads to L[f'] (s) = sL[f](s)-f(0)? O Change of variable O Integration by parts O Indefinite integration If L[h] (s) = L[f](s)L[g] (s), what do we know about h? (tick all that are true) Of is the convolution of g and h □h(t) = f f(tv)g(v)dv □ h = f*g □h(t) = f f(v)g(t – v)dv Which of the following gives the Laplace transform of f" = d²F\f(®) ds² $F[f](s)-f(0) s²Ff(s) sf(0) - f'(0) What is the correct expression for L[f"](s) when L[ƒ] = 5e-³², f(0) = 5 and f'(0) = 0? Sof(t)e-st dt □h(t) = f(t)g(t)
Transcribed Image Text:Core Laplace Which of the following represents the Laplace transform L[g](s) So g(t)est dt of f(t)e="tdt fog(s)e-st dt What integration technique leads to L[f'] (s) = sL[f](s)-f(0)? O Change of variable O Integration by parts O Indefinite integration If L[h] (s) = L[f](s)L[g] (s), what do we know about h? (tick all that are true) Of is the convolution of g and h □h(t) = f f(tv)g(v)dv □ h = f*g □h(t) = f f(v)g(t – v)dv Which of the following gives the Laplace transform of f" = d²F\f(®) ds² $F[f](s)-f(0) s²Ff(s) sf(0) - f'(0) What is the correct expression for L[f"](s) when L[ƒ] = 5e-³², f(0) = 5 and f'(0) = 0? Sof(t)e-st dt □h(t) = f(t)g(t)
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