Let f(x) = (e^x - 1)/x. Approximate lim x-->0 f(x)

Answer 1

(e^x - 1)/x

If x = 0, this evaluates to 0/0 which is ambiguous.

We can try L'Hopital's Rule: take the 1st derivative of top and bottom to get:

e^x / 1

Now when x goes to zero, the limit is 1.

CHECK by graphing the original function