- #1
jdcasey9
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Homework Statement
Give an example where f2 [tex]\in[/tex] R[tex]\alpha[/tex], but f[tex]\notin[/tex] R[tex]\alpha[/tex][a,b].
Homework Equations
Let [tex]\alpha[/tex]: [a,b][tex]\rightarrow[/tex] R(Real numbers) be increasing. A bounded function f: [a,b] [tex]\rightarrow[/tex] R(real numbers) is in R[tex]\alpha[/tex][a,b] if and only if, given [tex]\epsilon[/tex] [tex]\succ[/tex]0, there exists a partition P of [a,b] such that U(f,P) - L(f,P) [tex]\prec[/tex][tex]\epsilon[/tex].
The Attempt at a Solution
Would f(x) = (1/x)(sinx) work? Because (f(x))2 converges and f(x) diverges, right?