First slide

Introduction to limits

Question

The value of $lim_{x \to 0} \frac{x (5^{x} - 1)}{1 - \cos x}$ , is

Moderate

A

$5 \log 2$
B

$2 \log 5$
C

$\frac{1}{2} \log 5$
D

$\frac{1}{5} \log 2$

Solution

We have,
$lim_{x \to 0} \frac{x (5^{x} - 1)}{1 - \cos x} = lim_{x \to 0} \frac{(\frac{5^{x} - 1}{x})}{\frac{1 - \cos x}{x^{2}}} = 2 \ln 5$

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