Question: 3. Prove the following theorem: Theorem 2. Assume a > 0. Let f be continuous on [0, a]. Suppose for any 0 x a,

3. Prove the following theorem: Theorem 2. Assume a > 0. Let f be continuous on [0, a]. Suppose for any 0 x a, we have fo(t)dt = xf(x). Then there exists c ER such that f(x) = cx on [0, a]. Hint: Let h(x) = f(x) = X What is the derivative of h(x) if f is differentiable on (0, a)?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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

Students Have Also Explored These Related Mathematics Questions!

Why is the idea that value depends on consumers preferences radical?

Assume after completion of graduation you found a job which requires you to travel to different locations. You expect to clock around 12,000 miles per year. Hoping to save some money on the fuel...

Find the payback period for the following project: Project Y Initial Outlay $19,000 Year 1 $5, 290 Year 2 $5,090 Year 3 $ 5,620 Year 4 $ 7,620 The answer should be calculated to two decimal places

A local grocery chain reports that the annual consumption of fresh fruit per person is normally distributed with a mean of 46.25kg and a standard deviation of 3.5kg while the annual consumption of...

Q Search Problem 1 (4 pts): Evaluate the integral. 5x -4x +3x-2 dx x2 +1 Problem 2 (4 pts): Evaluate the integral by using the Integration by Parts method: St2 estz dt Problem 3 (4 pts): Integrate...

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...

MAT237Y, University of Toronto, 2017-8 Homework Assignment # 2 Preliminary material The homework assignment is found on the other side of this page. Our goal in this homework is to develop an...

MATH 135 S 2016: Assignment 9 Solutions 1. Prove that for any integer n, 441n43 + 374n35 + 285n23 0 (mod 55). Solution: Since 55 = 5 11 and gcd(5, 11) = 1, we may use the Splitting Modulus...

Kindly give only correct answers showing your steps 1. (a) Use the Intermediate Value Theorem to show that the equation - sin (x) + sin(x) =-1 has at least two distinct real solutions on (0, ce)....

Module 07 Short Answer Assignment - Functions, Domains, Ranges, 1-1, Onto - Answer Key Each graph represents a relation (A) F : X Y , that may also be a function. (B) X Y 1 (C) X (D) Y X Y 1X aY 1 a...

From a marketing perspective, what are the potential opportunities and challenges for Pedego Electric Bikes operating globally during the pandemic? (25 marks) Case study Impact of Covid-19 on E-bike...

Recall the Quimby case. This type of fraud is increasingly common. What could Quimby have done to protect himself?

y = 1 0 x 3 1 0 x - 2 + 9 determine the rate of change of y with respect to x

Calder, Inc. is a furniture manufacturing company with 50 employees. Recently, after a long negotiation with the local labor union, the company decided to initiate a pension plan as a part of its...

On January 1, Chreesh Corporation had 95,000 shares of no-par common stock issued and outstanding. The stock has a stated value of $5 per share. During the year, the following occurred. Apr. 1 Issued...

On January 1, Camel Cove Company issued $500,000, 10%, 10-year bonds at face value. Interest is payable semiannually on July 1 and January 1. Instructions Present journal entries to record the...

Jan Levinson is the owner of Levinsons Pizza. Levinsons is operated strictly on a carryout basis. Customers pick up their orders at a counter where a clerk exchanges the pizza for cash. While at the...

The following control procedures are used at Melora Company for over-the-counter cash receipts. 1. To minimize the risk of robbery, cash in excess of $100 is stored in an unlocked attach case in the...

Determine if the overhead allocated to the product relates to a single plantwide overhead rate method, multiple production department factory overhead rate method, or activity-based costing...

=+). The test statistic for the pooled t test is obtained by replacing both s1 and s2 in the two-sample t test statistic with sp where When the population distributions are normal with equal standard...

=+b. Does your method result in paired data?

=+c. Can you think of a reasonable method of collecting data that would result in independent samples? Would such an experiment be as informative as a paired experiment? Comment.