Question

Find the limit if it exists or show that the limit does not exist....

Answer 1

\[\lim_{(x, y) \rightarrow (0, 0)} \frac{x^{2}+y^{2}}{\sqrt{x^{2}+y^{2}+1}-1}\]

Answer 2

The answer is 2, but I can't figure out which function I need to use to approach it from. Because it's 2, I thought using y=x would work because it gives 2x^2 in the numerator, but the denominator still has the radical...

Answer 3

So going along y=x, you get:\[\lim_{x \rightarrow 0} \frac{2x^{2}}{\sqrt{2x^{2}+1}-1}\]

Answer 4

well rationalize the denominator simply..you'll get ans in the very next step..

Answer 5

I feel really stupid saying this, but I can't remember how to...

Answer 6

multiply and divide by \[\sqrt{2x ^{2} +1} +1 \]