Lab #4 Maclaurin Series In this lab, you will write a script to implement the Mclaurin Series You will need to show your lab professor to get your grades. Grades: 2% of your final course mark Deadline During the lab period of Week 10 (July 11) Steps Step 1. Maclaurin Series Maclaurin series are used to expand a function around zero. This series is an infinite series and is given as follows: C F7(0) n! xn flx) = n=0 where f(0) is the nt" derivative of f(x) evaluated at x = 0. Step 2. Exercise |tis found that Maclaurin series of f(x) = In(1 + x) is given as below: = Tn In(1+x) = Y (i n=1 Write the first six terms of this series, f,(x). Notice that the first value of nis 1 NOT 0. Write the first six terms of this series, f,(x). Notice that the first value of n is 1 NOT 0. Plot the original function f(x) against f,(x). * Write an R script that takes the value of x as an input from the user, then compute the value of the series for up to ten terms. For each term, find the absolute and relative error. Your output should look like the following table: n Absolute error Relative error =000 s U R N