Consider the function: () = ^2e^x^2 . a) Write the first five nonzero terms in the Taylor series expansion for () about = 0. You do not need to find the general term. Using a known Taylor series (from the pink sheet or the class notes), be sure to indicate which series you started with, and clearly show any modifications you made to it. b) Use your series from part a) to find the following derivatives: i) (4)(0) ii) (7)(0) iii) (8 )(0) c) Use the first three non-zero terms in your series from part a) to estimate the value of the following definite integral: ^2e^x^2 limit 0to 2