Question

Evaluate lim x—>infinity. x/(sqrt(x^2 - +1) ?

Answer 1

`1`.

Explanation:

`lim_(x to oo)x/sqrt(x^2+-1)`,

`=lim_(x to oo)x/sqrt{x^2(1+-1/x^2)}`,

`=lim_(x to oo)x/{xsqrt(1+-1/x^2)}`,

`=lim_(1/x to 0)1/sqrt(1+-1/x^2)`,

`=1/sqrt(1+-0)`,

`1`.