1. Find the Taylor polynomial p3 (x) for function f (x) = 4e-2x centered at a = 0. Use the Taylor polynomial P3 (x) to estimate 4e -0.2 . Formula: P3 (x) = f(a) + f'(a)(x - a) + f" (a) (x - a ) 2 + (a ) 2! 3 ! (x - a) 3. (8,2-) -301 . 2. Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the curve y = 2 cos(5x) on the given interval -~ , . Formula: L = So VI + [f' (x ) 12 dx. 3. Evaluate the following definite integral Jo x2-81 36 dx using the Partial Fraction Decomposition