Problem (1): Find the Laplace transform of the following time functions: Verify the answer using MATLAB (laplace 05)$ ): Note: $1(t)=u(t)=$ step function, and $\left({ }^{*} ight) denotes convolution. a) $f(t)=3+7 t+t^{2}+\delta(t)$, where $\delta(t)$ is the unit impulse function b) $f(t)=e^{-t}+2 e'{-2 t}+t e^(-3 t]$ c) $f(t)=1(t)+2 t \cos 2 t$ d) $f(t)=\sin ^{2} t+3 \cos ^{2} t$ e) $F(t)=\sin tx \sin t$ SP.SD.3331