Originally Posted by

**mosostow** Hi all,

Just wondering if I could get help with the following problem.

The question states that I have to prove that:

if lim(x->c) f(x) = L, then lim(x->c)|f(x)| = |L|

I've already proven the above. But then the question goes onto saying.

Show that the converse if false. Give an example where:

lim(x->c)|f(x)| = |L| and lim(x->c)f(x) = M where M is not equal to L.

Also, it asks to give an example where

lim(x->c)|f(x)| exists but lim(x->c)f(x) does not exist.

I'm a bit stumped with this, I can't think of one simple example. Any help would be appreciated.

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