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).

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Multivariable Limits

**Physics Forums | Science Articles, Homework Help, Discussion**