Help with Real analysis proof about limit laws and functions

[kbrono]

Homework Statement

Let f be a function let p /in R. Assume lim_x->p=L and L>0. Prove f(x)>L/2

The Attempt at a Solution

Let f be a function let p /in R. Given that lim_x->pf(x)=L and L>0. Since L\neq0 Let \epsilon= |L|/2. Then given any \delta>0 and let p=0 we have |f(x)-L| = |0-L| = |L| > |L|/2=\epsilon. Thus f(x) > |L|/2 near p.

 

[micromass]

Yes, this seems to be correct!

 

[kbrono]

Thank you!