Hi all.(adsbygoogle = window.adsbygoogle || []).push({});

I'm doing some self studying on limits, and...I have the following problem with this problem...

Prove: If [tex]f(x)>0[/tex] for all [tex]x[/tex], then [tex]\lim_{x\rightarrow x_o} f(x)\geq 0[/tex] for any [tex]x_o[/tex]

I'm assuming the best way to prove this is through contradiction:

Assume [tex]\lim_{x\rightarrow x_o} f(x) = A < 0[/tex]

This as far I get before vapor lock sets in. I guess I need to find an appropriate [tex]\epsilon[/tex] and then try to show/not show that [tex]f(x) < 0[/tex] for at least one [tex]x[/tex].

Can someone please point me on the right direction?

Thanks,

dogma

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Limit Proof

**Physics Forums | Science Articles, Homework Help, Discussion**