Question

limx→a x8-a8/x12-a12 answer evaluate​

Answer 1

Given

$\to\displaystyle \lim_{\sf x \to a} \sf \dfrac{x^8-a^8}{x^{12}-a^{12}}$

First of  check the  indeterminate form

Put x = a , on

$\sf\to \dfrac{x^8-a^8}{x^{12}-a^{12}}$

We Get

$\sf\to\dfrac{a^8-a^8}{a^{12}-a^{12}} = \dfrac{0}{0}$

it is 0/0 form so we use L'Hopital Rule

$\to\displaystyle \lim_{\sf x \to a} \sf \dfrac{\dfrac{d}{dx} (x^8-a^8)}{\dfrac{d}{dx} (x^{12}-a^{12})}$

$\to\displaystyle \lim_{\sf x \to a} \sf \dfrac{\dfrac{d(x^8)}{dx} -\dfrac{d(a^8)}{dx} }{\dfrac{d(x^{12})}{dx} -\dfrac{d(a^{12})}{dx} }$

$\sf \to\displaystyle \lim_{\sf x \to a} \sf \dfrac{8x^{8-1}-0}{12x^{12-1}-0}$

$\sf\to\displaystyle \lim_{\sf x \to a} \sf \dfrac{8x^{7}}{12x^{11}}$

$\sf\to \dfrac{8a^7}{12a^{11}} = \dfrac{2a^7}{3a^{11}} = \dfrac{2}{3a^4}$

Answer

$\sf\to\dfrac{2}{3a^4}$

Answer 2

Answer:

hopefully it will work ☺️☺️