Consider () = ^ sin() + cos(). Write a MATLAB script file to do the following:

A. Express each of the 3 elementary functions of () as polynomial coefficient vectors based on their Maclaurin series expansions. For each elementary function, include the first 4 terms of its series expansion in its polynomial coefficient vector.

B. Use built-in functions/operators to combine the 3 vectors into 1 polynomial coefficient vector that approximates (). Hint: You will need to pad one vector with 0s on the left.

C. Use built-in functions that operate on polynomial coefficient vectors to find (1), (0.3), and () 0.5 0 . Hint: Use the fundamental theorem of calculus to help evaluate the definite integral.

D. Compute the same values as the previous subpart using functions of the Symbolic Toolbox