Question

limx→∞ 5+sqrt(x2+5)/x−6

Answer 1

\[\lim_{x\to\infty}\frac{5+\sqrt{x^2+5}}{x-6}=\lim_{x\to\infty}\frac{\sqrt{x^2+5}}{x-6}=\lim_{x\to\infty}\sqrt{\frac{x^2+5}{x^2-12x+36}}\]\[=\lim_{x\to\infty}\sqrt{\frac{x}{x-6}}=1.\]

Answer 2

thanx! can u explane how did u get (sqrt(x^2+5)/(x^2-12x+36))

Answer 3

use L-Hospitals rule then you can easily find it out???

Answer 4

That's because\[\sqrt{x^2-12x+36}=x-6\]