Question 1 [2 x 3pts + 2 x 3pts] Compute the first three (nonvanishingontrivial) terms in the Taylor expansion for the following functions: a. f (x ) = (8+x)3/2 (i) about x = 0 and x = 9 b. f (x ) = 1/(8+ x) 1/2 (i) about x = 0 and x = 9 Question 2 [3 x 3pts] a. Show that (-1)n sin(x) = IM: x2n+1 (2n + 1)! b. Show that xn ex n! n=0 C. From (a) and (b) create the Taylor series for ex cosx. Question 3 [3x3 pts] a. Consider the product (1 -x) x = (1-x)(1 +x + x2 + ...+x) ); n=0 by multiplying out the right-hand-side, establish the geometric progression Exn=1-XN+1 1 - x (1) n=0 b. From Eq.1 show how we have the geometric series Ex for Ixl