# Complex Analysis Problems

## Question

1. If f:[a,b]->R is a bounded function such that f(x)=0 except for x E {c1, c2,..., cn} C [a,b]. Show that f is Riemann integrable on [a,b] and determine the Riemann integral value.

2. Suppose that f is any bounded function on [a,b] and that, for any number c E (a,b) the restriction of f to [c,b] is Riemann integrable. Show that f is integrable on [a,b] and that Integrate[a->b] f = Limit[c->a+] Integrate[c->b] f

3. Prove that the function f:[0,1]->R defined by f(0)=1, f(x)=0 if x is irrational, and f(m/n) = 1/n, if m,n E N are relatively prime is Riemann integrable.

## Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

\$20.00 for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Complex Analysis Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.