$lim x \to a \frac{x^{n} - a^{n}}{x - a}$

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Solution

We know that
$x^{n} - a^{n} = (x - a) (x^{n - 1} + a x^{n - 2} + . . . . a^{n - 1})$

Hence,after putting the expansion in numerator.and applying limit.

$lim x \to a \frac{x^{n} - a^{n}}{x - a} = n a^{n - 1}$

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