Only #3

2. Compute, by hand, approximations to f'(1) for each of the following functions, using h-1/16 and each of the derivative approximations contained in (2.1) and (2.5) (b) f(x) - arctan; (c) f(x) - sin; (d) f(x)-e (e) f(x)Inr 3. Write a computer program that uses the same derivative approximations as in the previous problem to approximate the first derivative at x - 1 foreach of the following functions, using h-1 -4, 8, 16, 32. Verify that the predicted theoretical accuracy is obtained-in other words, show that your results are consistent with the analysis in this section. (b) f(x) - arctanx; (c) f(x) - sinnz (d) f(x)-e (e) f(x) lnx