$\mathop {\lim }\limits_{x \to 0} \,\,\frac{{{e^{\tan x - {e^x}}}}}{{\tan x - x}} = $

JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Analyzing +4 | -1

\lim\limits_{x \to 0} \,\,\frac{{{e^{\tan x - {e^x}}}}}{{\tan x - x}} =

View answer and explanation

Correct option: A

Option A (1) is correct because after factoring out

e^x

and using the limit property

\lim_{x \to 0} \frac{e^x - 1}{x} = 1

, the limit simplifies to 1.

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