Question

Question #04f88

Answer 1

`1`

Explanation:

`x(sqrt(x^2+1)-sqrt(x^2-1))=(2x)/(sqrt(x^2+1)+sqrt(x^2-1))` and

`(2x)/(sqrt(x^2+1)+sqrt(x^2-1))=(2x)/(x(sqrt(1+1/x^2)+sqrt(1-1/x^2)))=`

`2/(sqrt(1+1/x^2)+sqrt(1-1/x^2))` so

`lim_(x->oo)x(sqrt(x^2+1)-sqrt(x^2-1))=lim_(x->oo)2/(sqrt(1+1/x^2)+sqrt(1-1/x^2))=2/2=1`