calculus: la place tranformations

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16 Terms

1
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f(x) = 1. What is L(1)s
1/s
2
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f(x) = x. What is L(f)s
1/s^2
3
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f(x) = x^n. What is L(f)s
n!/s^(n+1)
4
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f(x) = 1/(sqrt(pi)\*x). What is L(f)s
1/sqrt(s)
5
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f(x) = e^ax. What is L(f)s
1/(s-a)
6
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f(x) = xe^ax. What is L(f)s
1/(s-a)^2
7
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f(x) = x^ne^ax. What is L(f)s
n!/(s-a)^n+1
8
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f(x) = sin(ax). What is L(f)s
a/(s^2+a^2)
9
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f(x) = cos(ax). What is L(f)s
s/(s^2+a^2)
10
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f(x) = e^ax\*sin(bx). What is L(f)s
b/\[(s-a)^2+b^2\]
11
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f(x) = e^ax\*cos(bx). What is L(f)s
(s-a)/\[(s-a)^2+b^2\]
12
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f(x) = cosh(ax). What is L(f)s
s/(s^2-a^2)
13
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f(x) = sinh(ax). What is L(f)s
a/(s^2-a^2)
14
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what is L\[y′\](s) 
s L\[y\](s) − y(0).
15
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what is L\[y′′\](s)
s^2 L\[y\](s) − s y(0) − y′(0)
16
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what is L\[y′′’\](s)
s^3L(y)(s)-s^2y(0) - sy’(0) - y’’(0)