Free Printable General Fourier Series

1.

The Fourier series is a combination of -----and ---- trigonometric terms

a)

sine and co secant

b)

tangent and cotangent

c)

sine and cosine

d)

cosine and secant

2.

what is the coefficient of cosine in a Fourier series?

a)

a₀

b)

a_n

c)

b_n

d)

None of these

3.

Identify Even function from the following

a)

x+x²

b)

x² + x³

c)

x²

d)

1+x

4.

Identify odd function

a)

1+x+x²

b)

x+2

c)

x-x³

d)

x² +x⁴

5.

The Fourier constant b_nfor f(x)= x sinx in (-2,2) is

a)

2

b)

1

c)

0

d)

4

6.

The trigonometric Fourier series of an even function does not have

a)

Sine terms

b)

Cosine terms

c)

Constant term

d)

harmonic terms

7.

A Periodic function is given by a function which

a)

has a period T= 2π

b)

has a period T= π

c)

satisfies f(t+T) = f(t)

d)

satisfies f(t+T) = - f(t)

8.

If f(x) = sinh(x) defined in -π<x<π then a₀and a_n values are

a)

a₀ = 0 , a_n= 1

b)

a₀ = 1 , a_n= 1

c)

a₀ = 0 , a_n= 0

d)

a₀ = 1 , a_n= 1

9.

Which of the following functions cannot be expressed as a Fourier series ?

a)

tanx

b)

x

c)

xsinx

d)

cosx

10.

If\ b_n\ =\frac{4}{n\pi}\left\{1-\left(-1\right)^n\right\}\ ,\ What\ is\ the\ value\ of\ b_3\ ?

a)

$\frac{4}{n\pi}$

b)

$\frac{8}{n\pi}$

c)

$\frac{-8}{n\pi}$

d)

0

General Fourier Series

Total questions: 10

Worksheet time: 4mins

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