Let $f(x)=\displaystyle\lim _{\mathrm{n} \rightarrow \infty} \displaystyle\sum_{\mathrm{r}=0}^{\mathrm{n}}\left(\frac{\tan \left(x / 2^{r+1}\right)+\tan ^{3}\left(x / 2^{r+1}\right)}{1-\tan ^{2}\left(x / 2^{r+1}\right)}\right)$. Then $\displaystyle\lim _{x \rightarrow 0} \frac{\mathrm{e}^{x}-\mathrm{e}^{f(x)}}{(x-f(x))}$ is equal to