Recent content by jetsetjoe

Thanks! As we've proved [in my class] that continuous functions are integrable, I think this does hold.

Thanks, bel. Can you provide an example (where f^3 is integrable, but f isn't) to backup show the f^3 integrable does not imply f integrable? It's still not clear to me the way f^2 now is (if f is -1 on irrationals, 1 on rationals, f^2 would be integrable, but f wouldn't be, for example).

Homework Statement Let f:[a,b] -> R R being the set of real numbers If f^3 is Reimann-integrable, does that imply that f is? Homework Equations If f is Riemann-Integrable, then it has upper/lower step functions, such that the difference between the upper and lower sums is less...

Homework Statement Show that there exists a differentiable real function: (f(x))^5 + f(x) + x = 0 Homework Equations ?? definition of the derivative: lim (as x -> a) [f(x) - f(a)]/x-a The Attempt at a Solution Not really sure where to start...

Homework Statement Find the radius of converge of: \sum[SIZE="4"]x^{}(n choose k) Homework Equations Radius of converge = 1/limsup|an+1/an|, for power series: anx^n The Attempt at a Solution Tried rewriting (n choose k) as: n!/[k!(n-k)!] but where do I...