hi, how can i prove the attached function is bigger than 0, if p(x) not equal to 0.

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- Nov 20th 2009, 02:02 PMyht0251help on prove a integral is bigger than 0
hi, how can i prove the attached function is bigger than 0, if p(x) not equal to 0.

- Nov 20th 2009, 02:09 PMDrexel28
- Nov 20th 2009, 02:16 PMyht0251
- Nov 20th 2009, 02:18 PMDrexel28
- Nov 20th 2009, 02:21 PMyht0251
- Nov 20th 2009, 02:22 PMScott H
Is $\displaystyle p$ continuous?

Since $\displaystyle p(x)^2$ doesn't distinguish between the sign of $\displaystyle p(x)$, we may assume that $\displaystyle p(x)$ is nonnegative everywhere. Now, let's suppose that $\displaystyle c$ is a value at which $\displaystyle p(c)=L\ne 0$. By the assumed continuity of $\displaystyle p$, we have, from the epsilon-delta definition of limit,

For all $\displaystyle \epsilon$, there exists a $\displaystyle \delta$ such that $\displaystyle 0<|x-c|<\delta$ implies $\displaystyle |f(x)-L|<\epsilon$.

This just states that $\displaystyle \lim_{\small x\rightarrow c}f(x)=f(c)$.

What we need to do is find a way to show that there is some positive area under the curve $\displaystyle y=p(x)$. What happens when we let $\displaystyle \epsilon=\frac{L}{2}$? - Nov 20th 2009, 02:24 PMDrexel28
- Nov 20th 2009, 02:25 PMDrexel28
- Nov 20th 2009, 02:34 PMyht0251