dominated convergence theorem application (finding the dominating function)

what is the the integrable function gg over nonnegative real that dominates (n−x)n(n-x)^n? I was thinking using some sort of triangle ineq to get the function gg. However, if i do this, gg is dependent of nn also, which is something that i do not want to happen.

=================

1

Integrable…dominated… where?
– DonAntonio
2 days ago

nonnegative real
– dyyyyssss
2 days ago

? You mean the ray [0,∞)\;[0,\infty)\; ? With Lebesgue, Borel (the same here) measure…?
– DonAntonio
2 days ago

1

Well, (n−x)n(n-x)^n isn’t integrable over the non-negative reals for any nn, and furthermore {(n−x)n}\{(n-x)^n\} diverges pointwise for all x∈[0,∞)x \in [0, \infty), so I’m fairly certain that there is no function that dominates all (n−x)n(n-x)^n.
– Michael Lee
2 days ago

okay, coz, I was thinking of using dominated convergence to compute the integral of (n−x)n(n-x)^n over the non negative reals
– dyyyyssss
2 days ago

=================

=================