f and g are cont on [0,1], then f and g are integrable.
then both are continuous on [0,1], which implies that is differentiable on [0,1], and , for all (by a corollary to the FTOC)
1)This problem is for the younger kids give them a chance, please. Let be randomly chosen from (they can be the same). What is the probability that it is possible to find two real numbers that have their product equal to and their sum equal to . (By the way, "real", means non-imaginary).
2)Let be continous on so that for all . Prove that . (This is a classic).
I am sorry, I cannot follow.
That is not the Fundamental Theorem of Calculus.then both are continuous on [0,1], which implies that is differentiable on [0,1], and , for all (by a corollary to the FTOC)
Remember I am saying that:
, , , ...
would it be wrong to do this?
Obviously, the only way this integral can be zero for all x and all n is if . the result follows immediately.
Now i can see where the problem here would be, the "obviously" part.