Show that the limit of $f(x)$ as $x$ tends to infinity is unique. We tried looking this question up already but there did not appear to be any online solutions.
2026-04-13 09:44:58.1776073498
Unique solutions to infinite limits.
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Saying that $\lim_{x\to\infty} f(x)= L_1$ means "given any $\epsilon> 0$ there exist X such that if x> X then $|f(x)- L_1|< \epsilon$". Saying that $\lim_{x\to\infty} f(x)= L_2$ means "given any $\epsilon> 0$ there exist X such that if x> X then $|f(x)- L_2|< \epsilon$". Choose $\epsilon$ to be smaller than $\frac{|L_1- L_2|}{2}$ and show that those cannot both be true.