I am having a lot of trouble remembering some Laplace transform review. There ar

ID: 2987362 • Letter: I

Question

I am having a lot of trouble remembering some Laplace transform review. There are 4 questions posted and I would really appreciate any help!!

1. Evaluate L{5e^(4-3t))} using the definiton of the Laplace Tranform (i.e. limit)

2. Piecewise: Evaluate L{e^-t} from 0<_t< 2 and e^(2-t) on t >_ 2. Is it continuous?

3. Evaluate the Inverse Laplace L ^(-1) {3s/(2s^2 + 10)} using linearity

4. Same as above with L -1 { 5/ ((9s-1)^4)} I am having trouble with the partial fraction section on this one

1) L{5e^(4-3t))}

5e^(4-3t) is written as 5e^4*e^-3t so this is laplace transform of 5e^-4L(e^-3t)=5e^-4/(s+3) is laplace transform

2)1/(1+s)(1-1/(e^2(1+s))-1/(2+s)(1-1/e^2(2+s))+1/s+2

3)3/2 sin(sqrt5*t)

4)5(9t-1)^3/6

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