Problem 1:- Using sin(x) 2 2j+1)! x- derive a Taylor series for sin(x2 around x0 a. (3pts) Write a code which computes the Taylor series of sin(x2) using recursion and a tolerance based while loop approach. b. (4pts) On the interval [O, , plot the semi-log error in your approximation for tolerance values 10-4 , 10-6, and 10-8 C. (3pts) Describe your graphs and comment on any trends you observe. Problem 1:- Using sin(x) 2 2j+1)! x- derive a Taylor series for sin(x2 around x0 a. (3pts) Write a code which computes the Taylor series of sin(x2) using recursion and a tolerance based while loop approach. b. (4pts) On the interval [O, , plot the semi-log error in your approximation for tolerance values 10-4 , 10-6, and 10-8 C. (3pts) Describe your graphs and comment on any trends you observe