Hi there. Well, in the next exercise I must find the limit of [tex]\displaystyle\lim_{(x,y) \to{(0,0)}}{\displaystyle\frac{\cos(xy)-1}{x}}[/tex], if it exists. I wanna know if I did it right.(adsbygoogle = window.adsbygoogle || []).push({});

If [tex]y=cx[/tex]

[tex]\displaystyle\lim_{(x,y) \to{(0,0)}}{\displaystyle\frac{\cos(xy)-1}{x}}=\displaystyle\lim_{(x,y) \to{(0,0)}}{\displaystyle\frac{\cos(cx^2)-1}{x}}=\displaystyle\lim_{(x,y) \to{(0,0)}}{\displaystyle\frac{-\sin(cx^2)2cx-1}{1}}=-1[/tex]

If [tex]x=cy[/tex]

[tex]\displaystyle\lim_{(x,y) \to{(0,0)}}{\displaystyle\frac{\cos(cy^2)-1}{cy}}=\displaystyle\lim_{(x,y) \to{(0,0)}}{\displaystyle\frac{-\sin(cy^2)2cy-1}{cy}}=-\displaystyle\frac{1}{c}[/tex]

[tex]\therefore{\not{\exists}}\textsf{double limit}[/tex]

So, what you say?

By there, and thanks for posting.

PD: Ok, Now I see, after plotting with wolfram, some calculus errors I've committed. The limit actually seems exists. So I should use the delta epsilon definition of limits to make a demonstration.

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# Homework Help: Finding a limit R²->R

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