Question: If f is integrable on [-Ï, -] and a R, prove that linLf(x)sin(k+)xdx=0.

If f is integrable on [-Ï€, -] and a ˆˆ R, prove that
If f is integrable on [-Ï€, -] and a ˆˆ

linLf(x)sin(k+)xdx=0.

Step by Step Solution

★★★★★

3.43 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since sink x sin kx cos x cos kx sin x we have f... 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 (809).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

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

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:

If f is integrable on [a, b], prove that is of bounded variation on [a, b]. F(x)fo) dt

Q:

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

Q:

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Q:

Downloaded 02/28/15 to 132.174.255.3. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 15.7. Exercises 475 changes and we laugh no more. While...

Q:

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Q:

# 7 (chapter 5)(40 points, Due on Friday November 11) Question 1. [3 points each] Use the definition of Limit of functions to prove that x2 2 . 5 5 2 lim x 3 x 1 1 (B) x 1 (A) lim x 0 if x 2 2x (C)...

Q:

Feedback: #1: This is not the argument in this reading passage. (0/4). Question 1: Summarize the Riemann sum argument that gives the formula of area as a double integral. Hint 1: Read the subsection...

Q:

Question 1: Summarize the Riemann sum argument that gives the formula of area as a double integral. When computing these, you might have memories of Calculus I and finding the area of regions. This...

Q:

A survey determines that mint chocolate chip is the favorite ice cream flavor of 6% of consumers. An ice cream shop determines that of 240 customers, 18 customers stated their preference for mint...

Q:

Eclypso Inc. manufactures a product that passes through two processes: mixing and molding. All manufacturing costs are added uniformly in the mixing department. Information for the mixing department...

Q:

Which of these is / are most likely to help you reach your long - term wealth goals? i . start saving money early ii . start choosing the right stocks iii. employ extra education ( e . g . bachelor's...

Q:

A normal distribution has a standard deviation equal to 32. What is the mean of this normal distribution if the probability of scoring above x = 200 is .0228?

Q:

If g: Rn Rn and detg1 (x) 0, prove that in some open set containing we can write g = to gn 0 o g1, 0.., where is of the form gi(x) = (x1, Fi (x) , Xn), and T is a linear transformation. Show that we...

Q:

If M is a k-dimensional manifold with boundary, prove that M is a (k - 1) -dimensional manifold and M - M is a k=dimensional manifold.

Q:

Find a counter-example to Theorem 5-2 if condition (3) is omitted. Following the hint, consider f: (- 2, 2) R2 defined by

Q:

For each of the transactions below, record whether it would result in an increase or decrease in assets, liabilities, and net assets. Provide an answer for assets, liabilities, and net assets for...

Q:

Sort two employees based on their name, department, and age using the Comparator interface.

Q:

Convert totalDays to months, weeks, and days, finding the maximum number of months, then weeks, then days. Ex: If the input is 4 0 , then the output is: Months: 1 Weeks: 1 Days: 3