am confused about the coefficient for the sine term. Since similar previous questions I did, the coefficient for an, bn, or a0 is 1/L. Why is this 2/L? Why is that? Could you please explain? In what circumstance the coefficient will be 2/L? or 1/L?

am confused about the coefficient for the sine term. Since similar previous questions I did, the coefficient for an, bn, or a0 is 1/L. Why is this 2/L? Why is that? Could you please explain? In what circumstance the coefficient will be 2/L? or 1/L?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Question 4. Define the power series * 2k+1 2k +1 r2k+1 T(1):= L (2k + 1)² S(1) := k-0 (a) Show that…

A: We will use the basic knowledge of real-valued functions, series, and integral calculus to answer…

Q: y d 2d

Q: The question is to find a power series for the function centered at c f(x) = 5/(5-x) , c = -3

Q: Can you help me with the question in this picture? I have to find the Taylor series of the function…

Q: Example Find the fourier series of the periodic function sed.A. 1kt< 2

A: The Fourier series of the given periodic function has been obtained in step 2 and step 3.

Q: QUESTION 18 Determine the third order MacLaurin's polynomial for f(x) = ex.

A: Kindly note that I have authority to answer only one question. If you want remaining question to be…

Q: Fourier Sine and Cosine Series. In each of Problems 29 through 36: (a) Find the required Fourier…

A: (a) Consider the given function, fx=10<x<101<x<2 cosine series, period 4 here we need to…

Q: Find the first four nonzero terms of the Fourier cosine series of f. f(t)= Find the first four…

A: A function f(t) defined on an interval 0 < t < L is given.Find the Fourier cosine and sine…

Q: 2.4(a) Let f(x) = [1, 0, if0 < x < 1/2, if 1/2 ≤ x < 1. Find the Fourier cosine series for this…

A: Given function is fx = 1if 0 < x < 120if 12 ≤ x < 1…

Q: Fourier Sine and Cosine Series. In each of Problems 29 through 36: (a) Find the required Fourier…

Q: 31. f(x) = 1, 0≤x≤; cosine series, period 27

Q: 4.1. Find a power series representation for the function 8 using summation 2x-15 sign, 4.2.…

Q: x 3 = (a) Find the first 4 non-zero terms for the Maclaurin series for f(x). 3 1 + x + X 1+x² + 5 x…

A: Maclaurin series for (1-x)^(-1)= 1+x+ x^2 +x^3 +. . .. .

Q: Find (a) Fourier Sine Series, and (b) Fourier Cosine series for the function f(x) = |x| , 0 < x < L

Q: [1, -L < x < 0, 10, 0<x < L; f (æ + 2L) = f (x)

A: Fourier series

Q: Advance Engineering Mathematics subject about Fourier Series. show solution. Instructions: Find the…

Q: Half range Fourier seriesis defined as f(x)=2x within the range 0 <x <n a. Sketch Fourier sine…

Q: Is the given function even or odd or neither even nor odd? Find its Fourier series. Show details of…

A: From the given graph of fx, fx=-1-2≤x<010≤x≤2

Q: [1] period = 2π wwwwwww -π -π/2 (b) Find Fourier series a -π/4 π/4 π/2

Q: Q.3) Find Fourier cosine series and sine series of the function (0 < x < n/2) f(x) = 7/2 (7/2 < x <…

Q: Cos L S2

Q: pleasss solve this Find a_0 from the Fourier series of the function f(x)=1/4 (Tt-x)^2 * O T^2/4 none…

Q: Which of the following is the Fourier sine series of the function Select one: ∞ OA O B Oc O D. OE…

A: To find the fourier sine series of the function f(x)=3 on the interval 0<x<4, we need to…

Q: 6. Write the Fourier Sine series for f(x) =R - x (0<x<7). sin nx Ans. 2

A: To find the fourier sine series of the given function f(x) = π-x in half range 0 to π we use the…

Q: QUESTION 5 Solve the following two parts. (a) Write the Fourier series for cos? (x), x€l- n,m) even…

Q: Problem 4. Find a Fourier series for the function f(x) = x, 0 < x < 2. (Hint: Integrate the series…

Q: Find the Fourier series representation of the periodic function below if m= 6 and k = 15. Then,…

A: Given:The periodic function is given by if . It is given that and .To Find:We have to find the…

Q: (c) f(x) = x(10 – x), 0<x <10, Period = 10. From Fig. 7-9 below the funetion is seen to be even.…

Q: Find the Fourier series? 3. (Text Book Problem 7) Ax) =x-x+3, -2 s2

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Fourier Series. In each of Problems 11 through 16: (a) Sketch the graph of the given function for…

Q: 117X70 97 x 711- Xu!S O = (x)+

Question

This question is asking

(a) Find the required Fourier series for the given function.

(b) Sketch the function graph to which the series converges over three periods.

I am confused about the coefficient for the sine term. Since similar previous questions I did, the coefficient for an, bn, or a0 is 1/L. Why is this 2/L? Why is that? Could you please explain? In what circumstance the coefficient will be 2/L? or 1/L?

31. f (x) = 1, 0 < x < n; cosine series, period 27
Answer
O Solution
(a) L = T. For an even extension of the function, the sine coefficients are zero. The cosine coefficients are given by
2
f(x) dx =
dx = 2,
ao
L
and for n > 0,
dx
L
0.
an
COS
COS пх dr
The even extension of the given function is a constant function. As expected, the Fourier cosine series is
f(x) =
ao
:1.
2
(b)
2 1
65

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

1. Sketch the graphs of the following series on the interval x E [-3L,3L], and give a brief explanation of the differences between them: (a) The Fourier Series of the function f (x) = et calculated using the interval (-L, L). (b) The Fourier Sine Series of f(x) = e" calculated using the interval (0, L). (c) The Fourier Cosine Series of f(x) = e" calculated using the interval (0, L).
prove the following equation related to Fourier series, pls solve this ques within 20 minutes I'll give you multiple upvotes
Question 10. Find the Fourier cosine series forf (x) = x if 0≤x≤ 1/1/2 if / ≤x≤L on 0 ≤ x ≤ L.
hello , I am just going through homework answers my lecturer has written and have a question on the fourier series. when writing the values of an, a3 is negative. why is that ? and when he puts an into the equation he has turned sine to cosine.
Find Fourier cosine series and Fourier sine series of question 25 and 27. Sketch f(x) and two period extensions.
How would I do fourier (even) cosine series and fourier (odd) sine series on attached. I have to graph these too by hand and not sure how. This is piecewise function, Thanks so much
(a) Sketch the graph of the given function for three periods. (b) Find the Fourier series for the given function.
You want to find the Fourier series for the funtion tan(x) over the interval -2π to 2π. Will the Fourier series converge? Prove your answer quantitatively.
Investigate Taylor series expansion. Explain how the Taylor series is used in your calculator to compute values of functions such as sin(x) , cos(x) , and ex , where x represent any value. Write a brief report explaining your findings, and give examples.
(*) Find the Fourier cosine series of f(x) = sin(4x) on [0, π]. Could you guess what the Fourier cosine series of sin(8x) would be?
(a) Find the Fourier series of the 2?-periodic function ?(?)=?2 in−?<?< ?.(b) Find the Fourier integral of the function ?(?)={ ?, −2<?<2 0, else