Question

If limx→af(x)=L>0, then there is a δ>0 such that f(x)>0 when 0<|x−a|<δ. Please help me prove this!!

Answer 1

By definition of limit, for any epsilon>0 there exist δ such that for 0<|x−a|<δ, |f(x) -L| < epsilon. Choosing epsilon < |L-0| =|L| there have to exist a δ that makes |f(x) -L| < |L| > 0

Answer 2

Thanks for the help!

Answer 3

you wellcome