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JEE Previous Year Question

$Lt_{x \to 0} \frac{x 2 ^{x} - x}{1 - cos x} =$

Topic: JEE PYQ

Answer: B. Full step-by-step solution below.

A $\frac{1}{2}$
B $2 log 2$
C $log 2$
D $\frac{1}{2} log 2$

Correct answer: B

Solution

(b) : Lt_{x \to 0} \frac{x ( 2 ^{x} - 1 )}{1 - cos x} = Lt x \to 0 \frac{x ^{2}}{1 - cos x} \times Lt x \to 0 \frac{2 ^{x} - 1}{x} = 2 \times log 2

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