Let f(x) = lim_(n → ∞) Σ_(r=0)ⁿ ( (tan ( x/2^(r+1)) + tan³ ( x/2^… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 28 January, Shift 2Limits

Let $f(x) = \lim_{n \to \infty} \sum_{r=0}^{n} \left( \frac{\tan \left( \frac{x}{2^{r+1}} \right) + \tan^3 \left( \frac{x}{2^{r+1}} \right)}{1 - \tan^2 \left( \frac{x}{2^{r+1}} \right)} \right)$ Then, $\lim_{x \to 0} \frac{e^x - e^{f(x)}}{x - f(x)}$ is equal to:

A
$1$
B
$0$
C
$\infty$
D
$-1$

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