Let P be a polynomial of degree N. a) Show that P is of bounded variation on

Question:

Let P be a polynomial of degree N.
a) Show that P is of bounded variation on any closed interval [a, b].
b) Obtain an estimate for Var(P) on [a, b], using values of the derivative P'(x) at no more than TV points.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:04 AM

See More Questions

Let p() = (-1 )n(n - n-1n-1 -....- 1 - o) he a polynomial of degree n I (a) Show that if i, is a root of p() = 0 then i is an elgenvalue of C with eigenvector x = (in-1,, in-2...... i,1)T , (b) Use...
A circle and a line intersect at most twice. A circle and a parabola intersect at most four times. Deduce that a circle and the graph of a polynomial of degree 3 intersect at most six times. What do...
Let I n = x n e -x2 dx, where n is a nonnegative integer. a. I 0 = e -x2 dx cannot be expressed in terms of elementary functions. Evaluate I 1 . b. Use integration by parts to evaluate I 3 . c. Use...
Over the last few years, we have started to see some retailers open earlier and earlier on Thanksgiving Day. Others have taken a different approach and decide to remain closed. Is it a good strategy...
It has often been said that if the company cant earn a rate of return greater than the cost of capital, it should not make investments. Explain.
Paudel Limited has been in the retail business for many years and has reached its goal in securing a strong financial position. The board of directors decided that it is time to adopt a policy of...
True or False. The element mass matrices are always singular.
Before her death in 2009, Lucy entered into the following transactions. a. In 2000, Lucy borrowed $600,000 from her brother, Irwin, so that Lucy could start a business. The loan was on open account,...
6. A sender has the following data item to send: If 8-bit checksum is used 10011001111000100010010010000100 a. Find the checksum at the sender site. b. Find the checksum at the receiver site if there...
The Let's Read organization is a public charity under IRC Sec. 501(c)(3). It had total support of the following: United Way support................................. $ 10,000 Grant from the...
a) If is continuous on a closed nondegenerate interval [a, b], differentiate on (a,b), and if ' is bounded on (a, b), prove that is of bounded variation on [a, b]. b) Show that (x) = 3x is of...
Let be a function of bounded variation on [a, b] and be its total variation function. Prove that if is continuous at some point x0 (a, b), then is continuous at x0.
Which SQL statement would add a new field in the Employees table to a query? a. SELECT ALL FROM EMPLOYEES b. SELECT * FROM EMPLOYEES c. SELECT EACH FROM EMPLOYEES d. SELECT FROM EMPLOYEES
Trumpet and Trombone Manufacturing, Inc. prepares financial statements for the year just ended 9/30/2022. The company's general ledger and other financial reports show the following balances. Prepare...
Consider the following. T(x, y) = (x, y/3) (a) Identify the transformation. (b) Graphically represent the transformation for an arbitrary vector in R. 100 L
Calculate a) cost of goods sold, b) ending inventory, and c) gross margin for A76 Company, considering the following transactions under three different cost allocation methods and using perpetual...
A certain lake is stocked with 10,000 fish. The population is growing according to the logistics 10,000 curve: p where t is measured in months since the lake was initially stocked. 1 9e 5 a. Find the...
Consider the biochemical reactor X2 = |B+; B+yx + (1 -B- y)x X2 x = -( - 1)x 1)x + + ( - x)u [B+yx + (1 - By)x Let a = 23, p = 0.39, and y = 0.57. Construct and discuss the phase portrait in the x >...
Explain why the given statements are true for an acute angle . sin + cos > 1, if is acute.
If (x) 0 on the interval [a, b], the definite integral gives the exact area under the curve between x = a and x = b.
Continuation of Exercise 5-17. Determine the following: (a) P(X = 1|Y = 1) (b) P(X = 1, Y = 1|Z = 2) (c) P(X = 1|Y = 1, Z = 2)
Continuation of Exercise 5-17. Determine the conditional probability distribution of X given that Y = 1 and Z = 2.
Based on the number of voids, a ferrite slab is classified as either high medium, or low. Historically, 5% of the slabs are classified as high, 85% as medium, and 10% as low. A sample of 20 slabs is...
Seinfeld: The Apartment JERRY: Boys, boys. HAROLD: Oh, Jerry. JERRY: I slid the rent under your door, Harold. Did you get it? HAROLD: Yeah, yeah. Hey, Jerry, would you like anything from Mrs....
Let f be twice differentiable with f(0) = 6, f(1) = 8, and f'(1) = 7. Evaluate the following integral. [ = 0 0 xf" (x)dx
Bearwood Inc. completed Job No.D50 during 2021. The job cost sheet listed the following: Job No. D50 Costs for 12,000 units produced: Direct materials Direct labor Manufacturing overhead applied...

Let P be a polynomial of degree N. a) Show that P is of bounded variation on

Question:

Step by Step Answer:

a Since polynomials are C 1 on R they are of bounded variation on any a b b...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions