Problem 4 (4 points) Consider the function et 1 f(r) = (a) (3 points) Show that lim,0 f(x) = 1. Try to verify this empirically by computing f(x) for a = 10-k, k = 1, 2, ..., 15. Submit in a table your results in the form (exp(x)-1))/x error 1e-01 1.051709180756477 5.2e-02 1e-02 1.005016708416795 5.0e-03 where the error is |(e*1)/x-1|. Do your results agree with the theoretical expectations? Explain why. (b) (1 point) Repeat the above experiment, but now evaluate the alent expression e - 1 f(x) = document In(e=) Submit numerical results as in the above table. The second column should contain (e 1)/In(e") and the third column should contain |(e 1)/ In(e") 1|. (c) (Bonus 3 points) If the results in (b) are better than in (a), explain why