Answer by Julio Cáceres for How to prove that a limit is wrong using...
Remember the definition of limit, $$\forall \epsilon\; \exists \delta : |x-a|<\delta \rightarrow |f(x) - L|<\epsilon $$Now if $L$ is not the limit negate the definition, that is$$ \exists...
View ArticleAnswer by davidlowryduda for How to prove that a limit is wrong using...
You haven't given $\delta$ or $\epsilon$ in your proof. This is what you need to do.For instance, if you take $\epsilon = 1/2$, then you will never find a $\delta$ such that $\lvert x - 4\rvert <...
View ArticleHow to prove that a limit is wrong using Epsilon-Delta definition?
Suppose we have a function $f(x) = 9-x$. Now we know that $\lim\limits_{x\to4} f(x) = 5.$Using the $\epsilon - \delta$ definition:$|x-1| < \delta \implies |f(x) - 5| < \epsilon.$What if we take a...
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