Question

Find the limit:-
$\underset{x\to \infty }{lim}\frac{x^7-a^7}{x-a}$

Answer 1

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

Applying $L-$ Hospital Rule

$\underset{x\to \infty }{lim}\frac{7x^6}{1}$

D fining by $x^6$

$\therefore \underset{x\to \infty }{lim}\frac{x^7-a^7}{x-a}=0$

$\underset{x\to \infty }{lim}\frac{7}{x^6}$

Put $x=\infty$

$\frac{7}{x^6}\to 0$