Question: Prove that if f is integrable on [0,1] and > 0, then for all a 1/n lim

Prove that if f is integrable on [0,1] and β > 0, then

Prove that if f is integrable on [0,1] and β

for all a

1/n lim

Step by Step Solution

★★★★★

3.28 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let M sup x 01 fx By the Comparis... 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 (322).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

a) Suppose that gn > 0 is a sequence of integrable functions which satisfies Show that if f : [a, b] R is integrable on [a, b], then b) Prove that if f is integrable on [0,1], then tb lim gn (x) dx...

Q:

Let R = [a, b] Ã [c, d] be a two-dimensional rectangle and f: R R be bounded. a) Prove that for X = or X = L. b) Prove that if f is integrable on R, then c) Compute the two iterated integrals...

Q:

Let q Q. Suppose that a

Q:

2. (a) Prove that for each n E N, Pn := {~ : j = 0,1, ... ,n} is a partition of [0,1]. (b) Prove that a bounded function f is integrable on [0, 1] if (*) fo:= lim L (f, Pn ) = lim U (f, Pn ),...

Q:

11. [8 marks] Let / E R. Suppose that {an} converges to 4. Provide a complete and accurate e - N proof that {a? } converges to (2. BONUS [8 marks] Let I = Jo (vr + 1 - cos(2x)) da. Find the smallest...

Q:

Prove that if f is continuous on [0, 1] and satisfies 0 s f(x) 1 there, then f has a fixed point that is, there is a number c in [0, 1] such that f(c) = c.

Q:

1. (30%) True and False 1. Adr = [-1' , =-2 . 2. If f is continuous then _ _ f(t)dt = f(x). 2x -5 6x2 lim- lim - 1 49 x-27 x-9 3x- = 2 3. 4. The fact that f is an integrable function implies that...

Q:

Let A = : ne Zandn21 = 1737. Let f (z) = 0 if I E A 1 if re A In this question we will prove that f is integrable on [0, 1]. (a) Prove that 18 (f) = 1. (b) Prove that for every positive integer n,...

Q:

In each of the subproblems (2.1)-(2.3), construct a sequence of functions f : A -> R with the specified property, and explain why. 2.1. fn converges point-wisely, but not uniformly. 2.2. In converges...

Q:

4. Determine if each of the following statement is true or false. If it is true, prove it. If it is false, nd a counter example and explain why. (1) Given a function f : [0, 1] > R, if f2 is...

Q:

Nam Bounty Cookies Enterprise, NaBCE, is a registered SME that is specialised in bakery of banana bread, Cake break, apple bread etc. The enterprise is based in Ghana. It has recently acquired two...

Q:

A projectile is fired with initial speed v0 at an elevation angle of a up a hill of slope (a > ). (a) How far up the hill will the projectile land? (b) At what angle a will the range be a maximum?...

Q:

quities [ 3 Fullscreen Consider a company where the majority of its expenses are fixed costs, similar to Jenny's personal finance situation with her mortgage and necessities. If this company =...

Q:

(Present Value of an Annuity) Suppose you are hired by your state government to determine the profitability of a lottery offering a grand prize of $10 million paid out in equal annual installments...

Q:

4. Let f be integrable on [-n, n] and L E R. (a) Prove that if (O'Nf)(XO) ----; L as N ----; 00 and if (Sf)(xo) converges, then (SNf)(XO) ----; L. (b) Prove that M ~ 4(-1)ksinV2n sin v 2 n + 6 2 _ k2...

Q:

3. Let 00 ao ~ . S = 2 + 6(ak cos kx + bk sm kx) k=l be a trigonometric series and set for x E Rand N EN. Prove that S is the Fourier series of some continuous periodic function f : R ----; R if and...

Q:

2. If 1 : R --+ R is periodic on R and integrable on [-7f,7fJ, prove that the Cesaro means of S 1 are uniformly bounded; i.e., there is an M > 0 such that for all x E Rand N EN.

Q:

Perrin Company designs industrial prototypes for outside companies. Budgeted overhead for the year was $390,000, and budgeted direct labor hours were 26,000. The average wage rate for direct labor is...

Q:

12-24 Budgeted costs, kaizen improvements. Trendy T-Shirt Factory manufactures plain white and solid-colored T-shirts. Inputs include the following: Additionally, the colored T-shirts require 3...

Q:

Hart Labs, Inc. provides mad cow disease testing for both state and federal governmental agricultural agencies. Because the company's customers are governmental agencies, prices are strictly...