The correct option is C ma^m 1 x→ alimx^m a^m/x a =x→ alim(x a)(x^m 1+ax^m 2 + ...+ a^m 2x+ a^m 1)/x a = a^m 1+a^m 1+a^m 1+...+a^m 1 = ...

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Substitution Method to Remove Indeterminate Form

x→ alimxm-am/...

Question

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

m a^{m - 1}

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m a^{m}

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\frac{1}{m} a^{m}

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a^{m - 1}

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Solution

The correct option is C $m a^{m - 1}$
$lim x \to a \frac{x^{m} - a^{m}}{x - a}$
$= lim x \to a \frac{(x - a) (x^{m - 1} + a x^{m - 2} + . . . + a^{m - 2} x + a^{m - 1})}{x - a}$
$= a^{m - 1} + a^{m - 1} + a^{m - 1} + . . . + a^{m - 1}$
$= m a^{m - 1}$

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