Consider the function f(x) = ln(1 + x) a) Obtain Taylor series of f(x) around x = 0. Write down the procedure in detail, not just the final outcome. b) Write a MATLAB user-defined function that evaluates f(1), using Taylor series, for a given number of terms. For this purpose, first write a pseudo-code or step- by-step algorithm and include it in your submission. c) Test your program for increasing numbers of terms in the series. Create a plot that shows how many significant digits of precision you obtain in your answer as a function of the number of terms in the series. How many terms are necessary to reach machine precision (that is, order of ~ 10-6)?