Regarding limits in Real Analysis

[danielkyulee]

Question: Suppose that f(x)>0 on (0,1) and that lim as x goes to 0 exists for the function. Show that lim as x goes to 0 for the function is greater than or equal to 0.

So I know that intuitively that this is true for obvious reasons, but I can not think of a clever way to set up the proof for this problem.

Any ideas??

Thanks!

 

[Oster]

Say L is the limit for the function. Check the consequences of L being less than 0 using the epsilon delta definition of the limit.