Question

Lim f(x) 2^x-1/x. Find the limit of x as x approaches 0

Answer 1

The limit happens to be the derivative of
`2^x` at
`x=0`:

`\displaystyle f'(c) = \lim_(x\to c)(f(x)-f(c))/(x-c) \implies \lim_(x\to0) \frac{2^x - 1}x = (2^x)'\bigg|_(x=0) = \ln(2)\,2^x \bigg|_(x=0) = \boxed{\ln(2)}`