a)

b)

c)

d)

Aneeka Hunt
2021-01-27
Answered

Prove $F\left(s\right)=\frac{1}{s-2}\text{}\text{then}\text{}f\left(t\right)$ is

a)${e}^{2t}u\left(t\right)$

b)$u(t+2)$

c)$u(t-2)$

d)${e}^{-2t}u\left(t\right)$

a)

b)

c)

d)

You can still ask an expert for help

Derrick

Answered 2021-01-28
Author has **94** answers

Step 1

Given$F\left(s\right)=\frac{1}{s-2}$

We have to find the f(t)

Use definition of inverse Laplace transform, which is given below

$f\left(t\right)={L}^{-1}\left\{F\left(s\right)\right\}\dots \left(1\right)$

Step 2

Take inverse Laplace transform of$F\left(s\right)=\frac{1}{s-2}$

Hence,${L}^{-1}\left\{F\right\}\left(s\right)={L}^{-1}\left\{\frac{1}{s-2}\right\}\dots \left(2\right)$

From equation (1) and equation (2)

$f\left(t\right)={L}^{-1}\left\{\frac{1}{s-2}\right\}$

$={e}^{2t}u\left(t\right)$

Therefore,$f\left(t\right)={e}^{2t}u\left(t\right)$

Hence, option (a) is correct.

Given

We have to find the f(t)

Use definition of inverse Laplace transform, which is given below

Step 2

Take inverse Laplace transform of

Hence,

From equation (1) and equation (2)

Therefore,

Hence, option (a) is correct.

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