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Limits Continuity and Differentiability question

2025 · 28 Jan · Shift 2 · Q46

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JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 28 Jan · Shift 2 · Q46

Limits Continuity and Differentiability question

2025 · 28 Jan · Shift 2 · Q46

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

Let

f(x)=\lim \limits_{n \rightarrow \infty} \sum\limits_{r=0}^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

\lim\limits_{x \rightarrow 0} \frac{e^x-e^{f(x)}}{(x-f(x))}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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