Question #04f88

1 Answer
Cesareo R.
Mar 8, 2017

11

Explanation:

x(sqrt(x^2+1)-sqrt(x^2-1))=(2x)/(sqrt(x^2+1)+sqrt(x^2-1))x(√x2+1−√x2−1)=2x√x2+1+√x2−1 and

(2x)/(sqrt(x^2+1)+sqrt(x^2-1))=(2x)/(x(sqrt(1+1/x^2)+sqrt(1-1/x^2)))=2x√x2+1+√x2−1=2xx(√1+1x2+√1−1x2)=

2/(sqrt(1+1/x^2)+sqrt(1-1/x^2))2√1+1x2+√1−1x2 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

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