If we approach (0,2) through the curve $\alpha:\mathbb{R} \to\mathbb{R}^2, \alpha(t) = (\frac{5}{3} (t-2)^4,t)$ when $t\to2$, then the denominator vanishes. Does this allow us to conclude that the limit doesn't exist? If so, why?
2026-04-12 14:09:57.1776002997
Determining whether the limit $\lim_{(x,y)\to(0,2)} \frac{x(y-2)^3}{3x-5(y-2)^4}$ exists or not
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