First slide

Introduction to limits

Question

The value of $lim_{x \to 0} \frac{a^{x} - b^{x}}{x}$ is

Moderate

A

$\log (a / b)$
B

$\log (b / a)$
C

$\log (a b)$
D

$- \log (a b)$

Solution

We have,
$\begin{array}{l} lim_{x \to 0} \frac{a^{x} - b^{x}}{x} \\ = lim_{x \to 0} \{(\frac{a^{x} - 1}{x}) - (\frac{b^{x} - 1}{x})\} = \log (a) - \log (b) = \log (\frac{a}{b}) \end{array}$

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