Please label each part.

MATH 141 Homework 18 1. Find the Maclaurin series of each of the following functions. Write the first three nonzero terms as well as the full series using summation notation. (a) g(x) = 23 cos(23) (d) i(x) = / x3 cos(x3) dx. (b) h(x) = x sin(x2 ). (e) k(ze) = arctan(x) dx. (c) i(x) = x2 In(1 + x). (f) I(2) = x2e-27/2 dac. 2. Find the sum of each of the following series if they converge. 2n+1 2n (a) (-1)- 42n+1(2n + 1)! V2 n=0 2 (e) (-1)" (b) > (-1) n=0 (2n)! n = 0 (V3) 2n+1 (2n + 1) DO 1 (c) (-1) n1 (f) (-1)n- n = 0 n = 0 An (2n)! 18 1 (d) (-1) ( V3) 2n+1 (8) (-1) 2" n=0 2n + 1 5 7 n=0 3. Use "known" Maclaurin series to evaluate the following limits. cos x - 1+ 1x2 a) lim tan x - r cosx - 1x3 b) lim (c) Can you use these series to evaluate lim tan x - r cosx - 2x3 -? If not, why not? x-+3/2 25