$\epsilon$-$\delta$ 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
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Updated on September 24, 2022

Comments

  • HeyEverybody
    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.

    $$\lim_{(x,y)\rightarrow (0,0)} \frac{2x^2-3y^2}{\sqrt{x^2+y^2}} = 0 \>.$$

    I'm still getting used to deriving the delta-epsilon proof of a limit for functions of many variables, any help is really appreciated!