Limit of Trigonometric Series Function (JEE Mains) | ExamDuo

Special forms and miscellaneous limitsMedium

Limit of Trigonometric Series Function

Let $f(x) = \mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 0}^n {\left( {\frac{{\tan (x/{2^{r + 1}}) + {{\tan }^3}(x/{2^{r + 1}})}}{{1 - {{\tan }^2}(x/{2^{r + 1}})}}} \right)}$ . Then $\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - {e^{f(x)}}}}{{(x - f(x))}}$ is equal to ____.

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