Answer
$0.693$
Work Step by Step
Given $$\lim _{x \rightarrow 0} \frac{2^{x}-\cos x}{x}$$ Consider $$ f(x)= \frac{2^{x}-\cos x}{x}$$ From the following figure, we can observe that \begin{align*} \lim _{x\rightarrow 0^+} f( x)&=0.693\\ \lim _{x \rightarrow 0^-} f( x)&=0.693 \end{align*} Then $$\lim _{x \rightarrow 0} \frac{2^{x}-\cos x}{x}=0.693$$
