6. (a) Prove that if f is integrable on [0,1], then 1 n 1/2k r f(x) dx...

Question:

(a) Prove that if f is integrable on [0,1], then 1 n 1/2k r f(x) dx = lim L 1 f(x) dx. Jo n-oo k=O 1/2k+1

(b) Suppose that f is integrable on [a, b], Xo =

a, and Xn is a sequence of numbers in [a, b] such that Xn l' b as n ---; 00. Prove that Ib n l xk+1 a f(x) dx = nl~~ t; Xk f(x) dx.

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: 9780131453333

3rd Edition

Authors: William R. Wade

See More Books

Question Posted: Jul 18, 2024 07:09 AM

See More Questions

A vertical analysis is being conducted for TTG Ltd. TTG Ltd. Income Statement Year Ended December 31 2020 2021 2022 Revenue $ 732,000 $ 782,000 $ 832,000 Cost of goods sold 439,200 461,380 482,560...
You wish to determine the enthalpy of vaporizaton of species A. You are able to fi nd the following data: Species A has a normal boiling point of 207.3 K, and at 20.0 atm, it boils at 301.5 K. The...
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...
Consider wave-free laminar condensation on a vertical isothermal plate of length L, providing an average heat transfer coefficient of h L . If the plate is divided into N smaller plates, each of...
Refer to Exercise 6.5. a. Show that x is an unbiased estimator of . b. Find 2x-bar. c. Find the probability that x-bar will fall within 2 x-bar of . 4 p(x) .2 .3 .2 .2
The variable T ~B(n, 0.96) and it is given that P(T = n) > 0.5. Find the greatest possible value of n.
1. What are the major sources of consumer information?
Supply the missing information in the following table for Blair Company. Sales ........... $484,000 ROI .......... ? Operating assets ...... ? Operating income ..... ? Turnover ......... 2.2 Residual...
The following information relates to Hors Back Falls Ltd's inventory transactions during the month of February Units 9,200 5,900 Cost/Unit $29.00 Amount $237,800 Feb. 1 10 14 Beginning inventory Sale...
7. Let f : [a, b] ---; R, a = Xo < Xl < ... < Xn = b, and suppose that f(Xk+) exists and is finite for k = 0,1, ... , n-1 and f(Xk-) exists and is finite for k = 1, ... , n. Show that if f is...
Show that if f : [a, b] ---; R is integrable on [a, b], then lim Ib f(x)gn(x) dx = O. n---+oo a (b) Prove that if f is integrable on [0,1], then lim rl xnf(x) dx = O. n---+oo Jo
Compute and plot the magnitude and phase of the DFT of the following finite-length sequences: (a) $x(n)=2 \cos \left(\pi \frac{n}{N} ight)+\sin ^{2}\left(\pi \frac{n}{N} ight)$, for \(0 \leq n \leq...
When do we use Fourier transforms and Laplace transforms in RC/RL/RLC circuit analysis?
What are the protocols used in a drone?
How do we design a drone?
What are the different types of drones?
What are the applications of drones?
Use the information provided in BE12-1. Assume that at January 1, 2014, the carrying amount of the patent on Celine Dions books is $43,200. In January, Celine Dion spends $24,000 successfully...
The cash records of Holly Company show the following four situations. 1. The June 30 bank reconciliation indicated that deposits in transit total $720. During July, the general ledger account Cash...
eBook Question Content Area Payable Transactions Richmond Company engaged in the following transactions: Purchased $ 5 2 , 0 0 0 of supplies from ABC Supplies on February 1 6 . Amount due in full on...
How did you solve this problem-You just won $25,000 and deposited your winnings into an account that pays 6.2% interest, compounded annually. How long will you have to wait until your winnings are...
A portfolio manager summarizes the input from the macro and micro forecasters in the following table: Micro Forecasts Asset Expected Return ( % ) Beta Residual Standard Deviation ( % ) Stock A 2 2 1...

6. (a) Prove that if f is integrable on [0,1], then 1 n 1/2k r f(x) dx...

Question:

Step by Step Answer:

An Introduction To Analysis

Students also viewed these Business questions