- #1

twoflower

- 368

- 0

suppose I want to get this:

[tex]

\lim_{[x,y] \rightarrow [0,0]} (x^2+y^2)^{xy}

[/tex]

Here's how I approached:

[tex]

\lim_{[x,y] \rightarrow [0,0]} (x^2+y^2)^{xy} = \lim_{[x,y] \rightarrow [0,0]} \exp^{xy \log (x^2+y^2)}

\lim_{[x,y] \rightarrow [0,0]} xy \log (x^2 + y^2) = (x^2 + y^2) \log (x^2 + y^2) \frac{xy}{x^2 + y^2} \rightarrow 0

[/tex]

Because the last fraction is bounded and the part before it goes to 0 (I hope).

But that's the problem, I don't know how to prove

[tex]

\lim_{t \rightarrow 0+} t\ \log t = 0

[/tex]

Thank you for help.