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Compute the limit

Jamie

New member
Feb 11, 2014
17
Screen Shot 2014-03-06 at 1.30.14 PM.png

I got that the limit equals 0 by simplifying the denominator from:

((x2+y2+1)1/2) - 1

to
((x2 - (y+1)(y-1))1/2) - 1

then
((x2 - (y(1+1)(1-1))1/2) - 1

and then evaluating the limit by plugging in 0, getting 0/-1=0

is this correct? is there a better way to do it?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I get a different result by converting to polar. This result is confirmed by W|A. So, I suggest using polar coordinates...what do you find?
 

Jamie

New member
Feb 11, 2014
17
Could you explain in more detail? I don't think I understand what you mean
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Essentially, I used $x^2+y^2=r^2$ and the limit becomes:

\(\displaystyle \lim_{r\to0}\left(\frac{r^2}{\sqrt{r^2+1}-1} \right)\)

And then I rationalized the denominator. You could also at this point use L'Hôpital's Rule.