# Math Help - A limit proof

1. ## A limit proof

Hi,

I am having a hard time trying to prove this.

If,
lim f(x) = L and f(x)>0, then L>=0.
x->a

(I am supposed to prove it by contradiction)

2. Originally Posted by akolman
Hi,

I am having a hard time trying to prove this.

If,
lim f(x) = L and f(x)>0, then L>=0.
x->a

(I am supposed to prove it by contradiction)
If $L<0$ then there exists $\epsilon > 0$ so that $L+\epsilon < 0$. This means there exists $\delta > 0$ so that for all $0<|x-a|<\delta$ we have $f(x) < L + \epsilon < 0$ and so $f(x) < 0$ on $(a-\delta,a+\delta)\setminus \{ a\}$.