MATLAB code. Answer the question for parts (a) - (e) and answer the general conclusion.

10. For each of the following functions, compute the Laplace Transform. Then plot the Laplace Transform over the interval [0, 10]. (a) sin t. (b) et (c) cos t. (d) t cos t. (e) m(t) sint. On the basis of these graphs, what general conclusions can you draw about the Laplace Transform of a function? In particular, what can you say about the growth or decay of the Laplace Transform of a function? Can you justify your conclusion by looking at the integral formula for the Laplace Transform? (Hint: Look at the derivation of L(eat) at the beginning of Chapter 13.) 10. For each of the following functions, compute the Laplace Transform. Then plot the Laplace Transform over the interval [0, 10]. (a) sin t. (b) et (c) cos t. (d) t cos t. (e) m(t) sint. On the basis of these graphs, what general conclusions can you draw about the Laplace Transform of a function? In particular, what can you say about the growth or decay of the Laplace Transform of a function? Can you justify your conclusion by looking at the integral formula for the Laplace Transform? (Hint: Look at the derivation of L(eat) at the beginning of Chapter 13.)