Fourier Series Expansions

Which of the following is not Dirichlet’s condition for the Fourier series expansion?

• (x) is periodic, single valued, finite

• f(x) has finite number of discontinuities in only one period

• f(x) has finite number of maxima and minima

• f(x) is a periodic, single valued, finite

At the point of discontinuity, sum of the series is equal to ___________

• a) 1/2([f(x+0)–f(x−0)])

• 1/2([f(x+0)+f(x−0)])

• 1/4([f(x+0)–f(x−0)])

• 1/4([f(x+0)+f(x−0)])

What is the Fourier series expansion of the function f(x) in the interval (c, c+2π)?

• a0/2+∑∞n=1ancos(nx)+∑∞n=1bnsin(nx)

• a0+∑∞n=0ancos(nx)+∑∞n=0bnsin(nx)

• Eulers formula

• None of the above

Find an if the function f(x) = x – x^3.

• finite value

• infinite value

• zero

• can’t be found

Find bn if the function f(x) = x^2.

• finite value

• infinite value

• zero

• can’t be found

If the function f(x) is even, then which of the following is zero?

• an

• bn

• a0

• nothing is zero

If the function f(x) is odd, then which of the only coefficient is present?

• an

• bn

• a0

• everything is present

Find a0 of the function f(x)=√[(1−cosx)/2]

• 4/π

• 2/π

• π/4

• π/2

Find the sum of 1

1/2+1/3^2+1/5^2+……… using Fourier series expansion if f(x) = a when [0,π] and 2 π – x when [ π, 2 π].

• π^2/8

• π^2/4

• π^2/16

• π^2/2

What is the value of a0 if the function is f(x) = x3 in the interval 0 to 5?

• 25/4

• 125/4

• 625/4

• 5/4