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.