(a) Consider the function f(x)=(ex ?1)/x.
Use l’Hˆopital’s rule to show that lim f(x) = 1 when xapproaches 0
(b) Check this result empirically by writing a program tocompute f(x) for x = 10?k, k = 1,...,15. Do your results agree withtheoretical expectations? Explain why.
(c) Perform the experiment in part b again, this time using themathematically equivalent formulation, f(x)=(ex?1)/log(ex), evaluated as indicated, with nosimplification. If this works any better, can you explain why?
Please ignore the programming part. I am interested in knowingwhy this happens.
