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## Homework Statement

Examine lim (x,y) -> (0,0) of:

[itex]\sqrt{x^{2}+1} - \sqrt{y^{2}-1}[/itex]

[itex]\frac{\sqrt{x^{2}+1} - \sqrt{y^{2}-1}}{x^{2}+y^{2}}[/itex]

## The Attempt at a Solution

Tried variable sub:

[itex]\sqrt{x^{2}+1} = a, \sqrt{y^{2}-1} = b[/itex]

[itex]\frac{a - b}{a^{2}-b^{2}}[/itex]

(a -> 1, b -> 1 as x,y -> 0)

Still nasty

Tried polar coordinates:

[itex]\sqrt{1 + r^{2}cosθ} - \sqrt{1 - r^{2}sinθ}/r^{2}[/itex]

But I can't find a way for this limit to exist (which it is supposed to do according to the answers).