MathAnalysisCalculusMultivariable calculus

Multivariable limits

By definition (pt. 2)

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Let's say we have a suspicion that $\lim\limits_{\vec{x} \to \vec{0}} f(x,y)=L=0$ for a function $f(\vec{x})$ such that after simplifying $\|f(\vec{x})-L\|<\varepsilon$ , we get $\|\vec{x}\| + N < \varepsilon \quad;\quad N \in \mathbb{R}$ .

Can we say this limit exists?

Select one option from the list

Yes

Only if N=0

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