Can someone please help me with this? I'm totally stuck on this! Tried polar coordinates but that doesn't bring anything. Does someone has any suggestion?
Find $\lim_{{x, y \to 0}}(x^2+y^2)^{x^2y^2}=1$
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"Find"...or "prove"? – DonAntonio Apr 08 '16 at 22:09
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sorry Prove "Printing Errors" :) – suugii19 Apr 08 '16 at 22:12
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Use polar coordinates:
$$\lim_{(x,y)\to(0,0)}(x^2+y^2)^{x^2y^2}=\lim_{r\to0} r^{2r^4\cos^2\theta\sin^2\theta}=1$$
since it is similar to
$$\lim_{x\to0}x^{x^4}=\lim_{x\to0}e^{x^4\log x}=e^0=1$$
DonAntonio
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Now i get it. I tried polar coordinates but couldn't see similiarity which you refered. Thank you Joanpemo sincerely :) – suugii19 Apr 08 '16 at 22:25