Advanced calculus 2

[spider1731]

construct an example for each
(a) Two Riemann integrable functions whose composition is not Riemann integrable.
(b) Two non-Riemann integrable functions whose sum is Riemann integrable
(c) A non-negative function f:[0,infinity) -> R such that the integral from 0 to infinity of f(x)dx converges but the limit as x goes to infinity of f(x) does not exist.

 

[Deleted member 4993]

construct an example for each
(a) Two Riemann integrable functions whose composition is not Riemann integrable.
(b) Two non-Riemann integrable functions whose sum is Riemann integrable
(c) A non-negative function f:[0,infinity) -> R such that the integral from 0 to infinity of f(x)dx converges but the limit as x goes to infinity of f(x) does not exist.

It looks like you could not even start the problem.

To start - please tell us the properties of Riemann integrable functions.

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.