Question: If E0 E are Jordan regions in Rn and f: E R is integrable on E, prove that f is integrable on E0.

If E0 ⊂ E are Jordan regions in Rn and f: E → R is integrable on E, prove that f is integrable on E0.

Step by Step Solution

★★★★★

3.53 Rating (177 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let 0 and choose M 0 such that fx M for all x E Since f is ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

741-M-N-A-D-I (703).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

Suppose that E1, E2 are Jordan regions in Rn. a) Prove that if E1 E2, then b) Prove that E1 © E2 and E1 E2 are Jordan regions. c) Prove that if E1, E2 are nonoverlapping, then Vol(E1 E2) =...

Q:

Let E be a Jordan region in Rn. a) Prove that E and are Jordan regions. b) Prove that Vol(Eo) = Vol() = Vol(E). c) Prove that Vol(E) > 0 if and only if E 0. d) Let f: [a, b] R be continuous on [a,...

Q:

Prove the following special case of Theorem 12.29i. Suppose that E and E0 are a Jordan regions in Rn, and that f: E R is bounded. If f is continuous on E \ E0, then f is integrable on E.

Q:

4. (a) Let El C E be Jordan regions in Rn. If f : E --+ R is integrable on E, prove that f is integrable on E1 . (b) If f is uniformly continuous on a Jordan region E, prove that f is integrable on...

Q:

Suppose that E is a Jordan region in Rn and that f, g: E R is integrable on E. a) Modifying the proof of Corollary 5.23, prove that fg is integrable on E. b) Prove that f g and f g are integrable...

Q:

6. (a) Suppose that E is a Jordan region in Rn and that Ik : E --+ R are integrable on E for kEN. If Ik --+ 1 uniformly on E as k --+ 00, prove that 1 is integrable on E and (b) Prove that lim ( A...

Q:

7. Let E be a Jordan region in Rn and let I, 9 : E --+ R be integrable on E. (a) Modifying the proof of Corollary 5.23, prove that Ig is integrable on E. (b) Prove that 1 V 9 and 11\ 9 are integrable...

Q:

Let E be an open Jordan region in Rn and x0 E. If f: E R is integrable on E and continuous at x0, prove that 1 lim 0+ Vol(B, (xo)) JB, (xo) f dV = f(x0).

Q:

KINDLY PLEASE DIGITALIZED IT 11- Find the Area between the curve y=x(x-3) and the ordinates x=0 and x=5. Note: (hint) The Graph shows 2 regions. Get first the area of each region before adding it...

Q:

Kindly please digitalized the answer 1- Integrate the following. 1. fx'dx 2. JT 3. S(x2 - 2x + 5) dx 4. S(x + 2)5 dx 5. S1+ y2 2ydy 6. S cos(70 + 5) do 7. S ( x2 + 2x - 3)(x + 1) dx 11- Find the Area...

Q:

Can we say that this is an application of integration by parts?

Q:

Your company are offered a bank loan with an annual percentage ate (APR) of 5 percent with quarterly compounding. What is the effective annual rate (EAR) on this loan?

Q:

On meeting new workers assigned to the unit, what topics would the supervisor discuss first? Why?

Q:

What three factors can be decreased to increase power?

Q:

24 + 3.1 + (-44) + (-8.2) + 63

Q:

100t t

Q:

-1/7 - (-1/6)

Q:

Home / Courses IENCE 623.(SUMMER VAN-18) 1 Week 1 troduction Mini Our Percentage Change + Back to Week 1 Introduction On5 Maddef 100 You want to qualify for the 20% quarterly sales bonus at work. You...

Q:

STA 210 - Homework 11 Section IV. B. and Lab 11 Section IV. B. Questions 1) What is the z used to create a 95% confidence interval? 2) What is the level of significance for a 95% confidence interval?...

Q:

STA2023-G3-5-07052021-215C David Gonzalez & | 07/18/21 8:52 PM Test: Week 2 Test (4.1-4.5, 5.1-5.3, 10.1-10.2) Time Remaining: 02:17:42 Submit Test This Question: 5 pts 15 of 20 (6 complete) This...