I'm trying to show the following:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\lim_{(x,y) \to (0,0)} \frac{x^2 + \sin^2 y}{x^2 + y^2} = 1.

[/tex]

One can show that

[tex]

\frac{x^2 + \sin^2 y}{x^2 + y^2} \leq 1

[/tex]

for all [itex]x,y[/itex] because [itex]\sin y \leq y[/itex]. So, if you can bound this guy from below by something that goes to 1 as [itex](x,y) \to (0,0)[/itex], you should be in business by the Sandwich Theorem. But I have so far been unable to do that! Does anyone have any suggestions as to how to proceed?

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# A frustrating limit of a function f(x,y)

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