Answer by egreg for Small Proof $\lim_{x\to x_0}f(x)\leq \lim_{x\to x_0}g(x)$
You should mention that the “wrong” inequality would hold for at least one $x$: just choose $x$ with $0<|x-x_0|<\min(\delta_1,\delta_2)$.You can also do it without contradiction. Suppose $f$ and...
View ArticleSmall Proof $\lim_{x\to x_0}f(x)\leq \lim_{x\to x_0}g(x)$
Can I get a quick check to see if I have done this correctly.Limit proofAssume By contradiction that $L_1>L_2$. Let $\epsilon = \frac{L_1-L_2}{2}$ then, $\forall$ $\epsilon>0$ $\exists$...
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