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Limits
Standard Limits
JEE Main 2019
Grade 11

Question:

$\lim_{x \to 0} \frac{x(e^x - 1)}{1 - \cos x}$
(1) $0$
(2) $1$
(3) $2$
(4) $3$

Step-by-Step Solution

Key Concept: $\frac{x(e^x - 1)}{1 - \cos x} = \frac{e^x - 1}{x} \cdot \frac{x^2}{1 - \cos x} \to 1 \cdot \frac{x^2}{x^2/2} = 2$.
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Correct Answer: (3)

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