- #1
johndoe3344
- 29
- 0
I was presented with the two following questions:
[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).
[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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