Quote by vbplaya
also for lim x→c f(x)= L >0. prove that there exists and open interal (a,b) containing c such that f(x)>0 for all x ≠ c in (a,b)
do I just pick out numbers and plug them in? because I don't know what else to do.

If the limit exist then for any h>0 there exist an open interval such that
f(x)L<h for all x in the open interval
in particular if L>0 then there exist an open interval such that
f(x)L<L for all x in the open interval
or equivalently
0<f(x)<2L so that
0<f(x) on some open interval