Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53ce1657-b18a-4e5a-99aa-3e87bdade9e3%2F06b12db2-bba2-45b3-ab31-d0e786b5d64c%2F7dd04xo_processed.png&w=3840&q=75)
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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