Consider the function f(x) = x2e3x and two series: the Maclaurin series of f (x) and the Taylor series of f (x) centered at a = -1. Write out the first three non-zero terms of each series, and find the formula of each series. Malaurin series VUUI 18 (3x X 32 U ! 9 * 4 2 4 + + X ex Taylor Series ( a ) a = - 1 (x- a ) U ! fin ( - 1 ) = e' u = 0 5 Co ( x + 1 ) SO, n = 0 0 2 ex = gel *tin S ( - 1 ) + f ( - 1 ) (xxx + 1 ) + f " ( - 1 ) ( x +1 ) 1 = 0 n ! x e 3x _ ze" x 2 ( 3 *+ 1 ) 1 = 0 n ! . find first 3 ( terms (For problems 1 and 2, consider the coordinate triple (1, 4, -1). 1) Plot the point. (Please use the ENTIRE space here to draw a large graph) X 4 0 2) If that point is the center of a sphere, and the sphere intersects the origin, find the equation of the sphere. 0 ) ( X - 1) + (9- 4)+ (2+ 1 ) 2 = >* find r