Problem 3

Consider the function f(x) = (e^x 1)/x.

(a) Use lHospitals rule to show that lim x0 f(x) = 1. (b) Use Matlab to make a plot of f(x) versus x, for x = (2/3)^k (k = 1,2,...,100). For the plot use a log scale on the x-axis (type help semilogx and help plot for help). Do you observe the correct limiting behavior as x 0? If not, at about what value of x does the trouble begin? (You need to turn in a copy of the plot).