I was presented with the two following questions:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} \sin\frac{xy}{xy}[/tex]

and

[tex]\lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} \sin(\frac{xyz}{xyz})[/tex]

I figured I would do a simple substitution: let t = xy for the first one, and the limit becomes as t ->0, sin t /t would approach 1. The answer is right for the first one.

Why doesn't the same technique work for the second one? (The answer for the second one is 0).

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# Multivariable Limits

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