Evaluate lim(x→0) (2^x - 1)/x

Question

Evaluate \(\lim\limits_{\text x \to0}\left(\cfrac{2^{\text x}-1}{\text x}\right) \)

lim(x→0) (2^x - 1)/x 

Answer 1

To evaluate : \(\lim\limits_{\text x \to0}\left(\cfrac{2^{\text x}-1}{\text x}\right) \)

lim(x→0) (2^x - 1)/x 

Formula used: L'Hospital's rule

Let f(x) and g(x) be two functions which are differentiable on an open interval I except at a point a where

This represents an indeterminate form. Thus applying L'Hospital's rule, we get

Thus, the value of \(\lim\limits_{\text x \to0}\left(\cfrac{2^{\text x}-1}{\text x}\right) \) is In 2.