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Use laplace transforms to compute the solution to the

1. The Laplace transform of e-10t u(t) is?

2. The Laplace transform of (t2cos ωt ) u(t) is?

3. By using the Laplace transform, compute the convolution x(t) * v(t) of the two signals?where x(t)= e-3t u(t) and v(t) = (5sin t )u(t)

4. Compute the inverse Laplace transform of X(s) = 3s2+2s+1s3+5s2+8s+4 ?

5. Use Laplace transforms to compute the solution to the differential equation given below?Where y(t)=0 ;y(t)=1

6. Determine the final value of X(s)= 3s2+4s+1s4+3s3+3s2+2s ?

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