Limits to infinite

Feb 2010
98
0
Limits to infinite have always confused me. I was going to see if someone could maybe further explain them to me. Here is one of the problems from one of my tests earlier this year.

lim as x-> infinte (sqrt(x-1)-sqrt(x+1)) The answer = 0... but why?
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
Limits to infinite have always confused me. I was going to see if someone could maybe further explain them to me. Here is one of the problems from one of my tests earlier this year.

lim as x-> infinte (sqrt(x-1)-sqrt(x+1)) The answer = 0... but why?
\(\displaystyle \lim_{x \to \infty} (\sqrt{x-1} - \sqrt{x+1}) \cdot \frac{\sqrt{x-1} + \sqrt{x+1}}{\sqrt{x-1} + \sqrt{x+1}}
\)
 
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