(2) (a) Prove that if {fn} converges to f uniformly and each {fn} is Riemann integrable...

 

Transcribed Image Text:

(2) (a) Prove that if {fn} converges to f uniformly and each {fn} is Riemann integrable on [a, b], then f is Riemann integrable on [a, b] and rb lim [* fn(x) dx = f( f(x) dx. N1x a a (b) Find a sequence {gn} of Riemann integrable functions on [0, 1] that converges pointwise to a Riemann integrable function g, but {fo In (x) dx} does not converge to f g(x) dx. (2) (a) Prove that if {fn} converges to f uniformly and each {fn} is Riemann integrable on [a, b], then f is Riemann integrable on [a, b] and rb lim [* fn(x) dx = f( f(x) dx. N1x a a (b) Find a sequence {gn} of Riemann integrable functions on [0, 1] that converges pointwise to a Riemann integrable function g, but {fo In (x) dx} does not converge to f g(x) dx.

Answer rating: 100% (QA)

1 bet Jnl be a sequence of Rolimann Integrable functions o... View the full answer