hi, how can i prove the attached function is bigger than 0, if p(x) not equal to 0.
Since doesn't distinguish between the sign of , we may assume that is nonnegative everywhere. Now, let's suppose that is a value at which . By the assumed continuity of , we have, from the epsilon-delta definition of limit,
For all , there exists a such that implies .
This just states that .
What we need to do is find a way to show that there is some positive area under the curve . What happens when we let ?