Answer
$\approx 0.6931$
Work Step by Step
We have to evaluate the limit:
$\lim\limits_{h \to 0} f(h)$, where $f(h)=\dfrac{2^h-1}{h}$
We compute the value of the function $f$ for values of $h$ close to 0:
$f(0.01)\approx 0.69555501$
$f(0.001)\approx 0.69338746$
$f(0.0001)\approx 0.6931712$
$f(-0.01)\approx 0.69075046$
$f(-0.001)\approx 0.692901701$
$f(-0.0001)\approx 0.69312316$
We got $\lim\limits_{h \to 0} f(h)\approx 0.6931$
