Q4. A Fourier COSINE series is required for the function defined by f(x) = { n, 0 < x < n/3 0, n/3 < x < n } (a) Write down the period T and the frequency ?0 of the extended function. (b) Calculate the coefficients an = 2/T ?[0 to T] f(x) cos(n ?0 x) dx and simplify your answer.
Added by Esperanza H.
Close
Step 1
Step 1:** Given function: \(f(x) = \begin{cases} 0, & \text{if } 0 < x < \frac{n}{3} \\ 1, & \text{if } \frac{n}{3} < x < n \end{cases}\) ** Show more…
Show all steps
Your feedback will help us improve your experience
Shaiju T and 78 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the Fourier series of f(x). f(x) is periodic with period 2π. -π < x < π. Work done for this problem: a0 = 3/2 an = (3/π)(-1)^n bn = 2/n f(x) = (3/2) + Σ[(3/π)(-1)^n cos(nx) + 2/n sin(nx)]
Sri K.
Find the Fourier Sine series for the function defined by f(x) = { 0, 0 < x < n; 2n, n < x < 2n and write down, 1. The period T and the frequency w0 of the Fourier Sine series 2. The coefficients bn for n = 1, 2, 3, ...
Madhur L.
Obtain the Fourier series expansion of the periodic function f (x) of period 2̴̵̶̷̸̡̢̧̨̛̖̗̘̙̜̝̞̟̠̣̤̥̦̩̪̫̬̭̮̯̰̱̲̳̹̺̻̼͇͈͉͍͎̀́̂̃̄̅̆̇̈̉̊̋̌̍̎̏̐̑̒̓̔̽̾̿̀́͂̓̈́͆͊͋͌̕̚ͅ͏͓͔͕͖͙͚͐͑͒͗͛ͣͤͥͦͧͨͩͪͫͬͭͮͯ͘͜͟͢͝͞͠͡ℼ defined by: f (x) = { -x -π < x < 0 ; x 0 < x < π, f (x) = f (x + 2π)
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD