Give an example of a function $\displaystyle f: [0,1] \to R $ such that $\displaystyle f \in R[0,1] $ [i.e f is Riemann integrable over [0,1]] $\displaystyle , f(x)>0, \ \forall x \in [0,1] , \ but \ \frac{1}{f} $ is not in $\displaystyle R [0,1] $

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- Feb 16th 2010, 09:05 AMflower3give an example
Give an example of a function $\displaystyle f: [0,1] \to R $ such that $\displaystyle f \in R[0,1] $ [i.e f is Riemann integrable over [0,1]] $\displaystyle , f(x)>0, \ \forall x \in [0,1] , \ but \ \frac{1}{f} $ is not in $\displaystyle R [0,1] $

- Feb 16th 2010, 09:12 AMtonio
- Feb 16th 2010, 12:45 PMDrexel28