Question

Evaluate: $\underset{x\to a}{lim}\frac{x^{14}-a^{14}}{x^{-7}-a^{-7}}$

Answer 1

$\underset{x\to a}{lim}\frac{x^{14}-a^{14}}{x^{-7}-a^{-7}}$

We know that,

$\underset{x\to a}{lim}\frac{x^m-a^m}{x^n-a^n}=\left(\frac{m}{n}\right)a^{m-n}$

$\Rightarrow \underset{x\to a}{lim}\frac{x^{14}-a^{14}}{x^{-7}-a^{-7}}=\frac{14}{-7}\left(a^{14-(-7)}\right)$

=$-2a^{21}$