Standard limits: $\dfrac{x^n - a^n}{x - a}$ and $\dfrac{\sin x}{x}$

Unit 13 · Limits

Prove and use the two standard limits $\lim_{x\to a} \dfrac{x^n - a^n}{x - a} = n a^{n-1}$ for rational $n$ and $\lim_{x\to 0} \dfrac{\sin x}{x} = 1$.