Let $A\subseteq R$ , $f:A\rightarrow R$ be a function and a be an accumulation point of $A$. Show that if $b\in R$ and $\lim_{x\rightarrow a}f\left(x\right)=b$ then $\lim_{x\rightarrow a}\left|f\left(x\right)\right|=\left|b\right|$. Feel like Heine definition is needed but unsure.
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$\begingroup$ Here's a MathJax tutorial :) $\endgroup$– ShaunDec 5, 2017 at 20:59
1 Answer
Hint: $\left|\left|f\left(x\right)\right|-\left|b\right|\right|\leq\left|f\left(x\right)-b\right|$ by the reverse triangle inequality.