Question

______________PROVE !!​

Answer 1

$\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}⋆$

》hence proved ✔✔

Answer 2

$\lim _{x\to \:a}\left(\frac{x^n-a^n}{x-a}\right)=na^{n-1}$

$\lim _{x\to \:a}\left(\frac{x^n-a^n}{x-a}\right)$

$\mathrm{Apply\:L'Hopital's\:Rule}$

$=\lim _{x\to \:a}\left(\frac{nx^{n-1}}{1}\right)$

$\mathrm{Simplify}$

$=\lim _{x\to \:a}\left(nx^{n-1}\right)$

$\mathrm{Plug\:in\:the\:value}\:x=a$

$=na^{n-1}$