Math 152 Week 13 Workshop Problems Write up your solutions to each of these problems on a seperate sheet of paper. sin(x) 1. Let f(x)= Also, define f(0) = 1. I 4/8/24 (a) Using known Maclaurin series and power series operations, find the Maclaurin series for f(x). (b) The sine integral is defined by Si(z) = f(t) dt. Find the Maclaurin series for Si(z) (c) Use the first two non-zero terms of your series from part b) to approximate Si(0.5). 2. Using power series, evaluate lim x ln(1 + 2x³) 2-0 1- cos(3x2) 3. Consider the series 1 1 A). 3.3 32.5 + 33.7 (a) Find a formula for a general term of this series. (b) Using the Alternating Series Error Estimation Theorem, determine the error in using the first 3 terms of the series to approximate the sum of the series. (c) Find the exact value of the sum of the series.