PLEASE PROVIDE CODE IN PYTHON.

(a) (15\%) Write and run a computer program to approximate the derivative of function f at point x defined by the equation f(x)=limh0hf(x+h)f(x). Try f(x)=sin(x) at x=0.5 and hn=0.5hn1,h0=1,n=1,2,,30. Compute absolute errors of the approximation using the formula error =y f(x), where yn is yn is an output of the program in iteration n. Plot the errors on using a log-scale, i.e., the axes of the plot should be log10 error versus log10h. Analyze the results. Repeat the same experiment for f(x)=x1. (b) (5\%) Find a way to calculate accurate values for f(x)=x21+x21xtan(x)x2sin(x). Determine limx0f(x). Hint: Use Taylor series expansions sin(x)tan(x)=x3!x3+5!x5=x+3x3+152x5+