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5 problems regarding Laplace transform

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1. Calculate the Laplace transform of exp(-10t) x u(t)

2. Calculate the convolution of exp(-t) and sin(t) using (a) the Laplace transform (b) direct integration

3. Compute the inverse transform of (3s^2 + 4s + 1) / (s^4 + 3s^3 +3s^2+2s)

4. Use Laplace transform to calculate the solution to the ODE y"+6y'+8y=u(t) y(0)=0 y'(0)=1

5. Determine the final value of (3s^2 + 4s + 1) / (s^4 + 3s^3 +3s^2+2s)

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