Recent content by Halen

how would you integrate (1+x^30)/(1+x^60) from 0 to 1? tried so many ways but in vain.. any help?

thank you! finally! :)

so there does not exist a point such that f(c)=e because it is irrational but we are told f(x)eQ? and so f is constant

i really hope I'm right now.. :) is it f(x)eQ?

oh yes.. sorry!

the function f is continuous and has a domain and range in the reals.

the question states: suppose that f:(0,1)--->R is a (strictly) increasing function. suppose also that there is a constant MeR such that f(x)<M for xe(0,1). prove that the left limit of f exists? how would you use the information about the function being strictly increasing? Thank you!

ohh.. the contradiction would be that f(c) is rational but e is not..

thank you! that is great help indeed! i have started the proof.. am i going on the right track? suppose there exists a,b e R such that f(a), f(b) e Q. WLOG, f(a)<f(b) Between any two rational numbers, there is an irrational number, say e such that f(a)<e<f(b) by IVT, there exists ce(a,b) such...

no, unforunately, i don't do topology.. but i can try answering the question.. Has it anything to do with f(Q) being countable?

The question states: Suppose that f:R--->R is continuous and that f(x) in the set Q (f(x)eQ) for all x in the Reals (xeR) Prove that f is constant. How would you go about this question? Any help is appreciated! i know we have to prove that f(x) is equal to some constant (p/q) ; q not...

Thank you! Helps indeed! So do you suggest that i solve it separately for the two cases of x?

X is a random variable with a continuous distribution with density f(x)=e^(-2|x|), x e R How would you calculate E(e^(ax)) for a e R? Will it be right to take a certain range of a? And also, can you take the bounds for the integral to be between -Infinity and Infinity?