Complex limit $e^{1/z^2}$ at $z=0$

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How can I calculate this limit?

I tried using Riemann sphere to show that $\lim1/(e^{1/z^2})= 0$ and then the limit is infinite, but is this correct?

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If $z\in\mathbb R$, the limit is $\infty$, but if $z\in\{xi\,|\,x\in\mathbb{R}\}$, the limit is $0$. Therefore, that limit doesn't exist.