Free Printable Fourier series

1.

A Fourier series is an expansion of a periodic function f(x) in terms of ...

a)

an infinite sum of sines and cosines

b)

an infinite sum of polynomials

c)

an infinite sum of exponents

d)

None

2.

Dirichlet conditions involves..(pick all correct answers)

a)

f must have a finite number of discontinuities in any given bounded interval

b)

f must be periodic and single valued

c)

f must have a finite number of maxima and minima

d)

None

3.

If f(-x)=f(x) ,then f is ....

a)

Both Odd and Even function

b)

Even function

c)

Odd function

d)

Neither even nor odd

4.

If f(-x)=-f(x) ,then f is ....

a)

Both Odd and Even function

b)

Even function

c)

Odd function

d)

Neither even nor odd

5.

$\int_{-1}^1\left(x^2\sin\left(3x\right)\right)dx=$

(a)

6.

If f(x) is odd then its Fourier series contains sine terms only. True or False

a)

True

b)

False

c)

Depends on the interval

7.

If f(x) is even, then....

a)

f(x)=0

b)

$a_n=0$

c)

$a_0=0$

d)

$b_n=0$

8.

Fourier series of $\sin^3x\ is..$

a)

3/4 sin x - 1/4sin 3x

b)

sinx+cosx

c)

3/4 cos x - 1/4sin 3x

d)

3/4 sin x - 1/4cos3x

9.

Which among the following are even functions?(pick all correct answers)

a)

cos(3x)

b)

|x|

c)

sin(3x)sin(x)

d)

xsin(x)

10.

$\frac{a_0}{2}+\sum_{n=1}^{\infty}\left[a_n\cos\left(nx\right)+b_n\sin\left(nx\right)\right]$ is...

a)

Fourier series of a function with period 2

b)

Fourier series of a function with period $\pi$

c)

Fourier series of a function with period $2\pi$

d)

None

Fourier series

Total questions: 10

Worksheet time: 4mins

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