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 - The Fusion of Science and Community**

# Multivariable Limits

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

Have something to add?

- Similar discussions for: Multivariable Limits

Loading...

**Physics Forums - The Fusion of Science and Community**