1. Use Theorem 7.1.1 to find ℒ{f(t)}. (Write your answer as a function of s .) f(t) = 6t 5 ℒ{ f ( t )} = 2. Use Theorem 7.1.1 to find ℒ{f(t)}. (Write your answer as a function of s .) f(t) = e t...

1. Use Theorem 7.1.1 to find

ℒ{f(t)}. (Write your answer as a function of
s.)

f(t) = 6t⁵

ℒ{f(t)} =

2. Use Theorem 7.1.1 to find

ℒ{f(t)}. (Write your answer as a function of
s.)

f(t) = e^t cosh t

ℒ{f(t)} =

3. Use Definition 7.1.1,

DEFINITION 7.1.1 Laplace Transform

Letf be a function defined for

t ≥ 0.

Then the integral

ℒ{f(t)} =

is said to be theLaplace transform off, provided that the integral converges.

to find

ℒ{f(t)}.

(Write your answer as a function ofs.)

f(t) =

cos(t),		0 ≤ t <>
0,		t ≥ ?

ℒ{f(t)} = (s > 0)

Jun 05, 2022

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