The question:
Let f: D-> R and let c be an accumulation point of D. Suppose that lim_x->c f(x)=L.
Prove that lim_x->c |f(x)|=|L|.
A sketch of what I have:
Definition of limit and then
|f(x)-L|<
||f(x)|-|L|| |f(x)-L|<
But I'm sketchy on the reasons and if this is the right direction. Any ideas? Thanks.