$\epsilon$$\delta$ proof of a limit of a function $f(x,y)$
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You have $$ f(x,y)\leq \frac{2x^2+3y^2}{\sqrt{x^2+y^2}}\leq \frac{3x^2+3y^2}{\sqrt{x^2+y^2}}=3\sqrt{x^2+y^2}. $$ Now you can apply the $\epsilon\delta$ procedure.
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HeyEverybody
Updated on September 24, 2022Comments

HeyEverybody 9 months
I was working on this exercise to prove the differentiability of a function at a certain point, but I got stuck in proving the following limit.
$$\lim_{(x,y)\rightarrow (0,0)} \frac{2x^23y^2}{\sqrt{x^2+y^2}} = 0 \>.$$
I'm still getting used to deriving the deltaepsilon proof of a limit for functions of many variables, any help is really appreciated!