Using the X - definition, how must you prove that: $$\lim_{x\to2} \frac{x}{(x-2)^2}=+∞$$
Can anyone please outline the method you used to solve this problem? Thank you in advance.
2026-03-29 14:01:46.1774792906
Using the X - Definition To Solve Limits
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One way to make this easier is if you commit to making $\delta \le 1$. If that is the case, then $$0 < |x - 2| < \delta \implies |x - 2| < 1 \implies x > 1.$$ So, under this assumption, $$\frac{x}{(x - 2)^2} > \frac{1}{(x - 2)^2}.$$ Is that enough to help you start?