Free Printable Revision Unit 3 C

1.

The Fourier Sine Transform of

e-^{ax}

a)

$F_s\left[e-^{ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{a}{a^2+s^2}$

b)

$F_s\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}$

c)

$F_c\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}$

d)

none of the above

2.

The Fourier cosine Transform of

e-^{ax}

a)

$F_s\left[e-^{ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{a}{a^2+s^2}$

b)

$F_s\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}$

c)

$F_c\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{a}{a^2+s^2}$

d)

none of the above

3.

\int e^{ax}\ \cos bx\ dx\ =

a)

$\frac{e^{ax}}{a^2+b^2}\left[a\cos bx-b\sin bx\right]$

b)

$\frac{e^{ax}}{a^2+b^2}\left[a\cos bx+b\sin bx\right]$

c)

$\frac{e^{ax}}{a^2+b^2}\left[b\cos bx+a\sin bx\right]$

d)

none of the above

4.

\int e^{-ax}\ \sin sx\ dx\ =

a)

$\frac{e^{ax}}{a^2+s^2}\left[a\cos sx-s\sin sx\right]$

b)

$\frac{e^{ax}}{a^2+b^2}\left[a\cos bx+b\sin bx\right]$

c)

$\frac{e^{-ax}}{a^2+s^2}\left[a\cos sx-s\sin sx\right]$

d)

$\frac{e^{-ax}}{a^2+s^2}\left[-a\cos sx-s\sin sx\right]$

5.

The value of

e^{\infty}

is------------------

(a)

6.

SinA sin B=

a)

$\frac{1}{2}\left[\sin\left(A+B\right)+\sin\left(A-B\right)\right]$

b)

$\frac{1}{2}\left[\sin\left(A+B\right)-\sin\left(A-B\right)\right]$

c)

$\frac{1}{2}\left[\cos\left(A+B\right)+\cos\left(A-B\right)\right]$

d)

$\frac{1}{2}\left[\cos\left(A-B\right)-\cos\left(A+B\right)\right]$

7.

The Fourier Sine Transform of

e^{-5x}

a)

$F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{5}{5^2+s^2}$

b)

$F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{5^2+s^2}$

c)

$F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}$

d)

none of the above

8.

The Fourier Cosine Transform of

e^{-5x}

a)

$F_c\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{5}{5^2+s^2}$

b)

$F_c\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{5^2+s^2}$

c)

$F_c\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{5}{a^2+s^2}$

d)

none of the above

9.

The Fourier sine Transform of f(x) is $F_s[f(x)]=$

a)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ dx\ =\ F_s\left[s\right]$

b)

$\frac{1}{\sqrt{2\pi}}\int_0^{\infty}f\left(x\right)\ \sin sx\ dx\ =\ F_s\left[s\right]$

c)

$\sqrt{\frac{2}{\pi}}\int_0^{\infty}f\left(x\right)\ \sin sx\ dx\ =\ F_s\left[s\right]$

d)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ \ \cos sx\ dx\ =\ F_s\left[s\right]$

10.

The fourier sine transform is linear

a)

True

b)

False

Revision Unit 3 C

Total questions: 10

Worksheet time: 5mins

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