# $\displaystyle \large \lim_{x \,\to\, a} \dfrac{x^n-a^n}{x-a}$ formula

## Formula

$\displaystyle \large \lim_{x \,\to\, a} \dfrac{x^n-a^n}{x-a} = n.a^{n-1}$

$x$ is a variable. $a$ and $n$ are constants. The value of a special algebraic expression $\dfrac{x^n-a^n}{x-a}$ as the value of $x$ approaches $a$ is written in limit form in calculus. It is often used as limit rule.

### Proof

Learn how to derive limit of $\dfrac{x^n-a^n}{x-a}$ as $x$ approaches $a$ in calculus.