mcode.sty Demo
Florian Knorn, florian@knorn.org
April 16, 2014
NOTE BEFORE YOU START
All that this package does is to congure the listings
package for you. If anything is not working the way you
want it, refer to the listings documentation rst and /
or ta

CHAPTER 17 TRIGONOMETRIC IDENTITIES AND EQUATIONS
EXERCISE 76 Page 190
1. Prove the identity: sin x cot x = cos x
L.H.S. = sin x cot x = sin x
2. Prove the identity:
1
cos x
sin x
tan x
sin x
= cosec
1
= cos x = R.H.S.
(1 cos 2 )
L.H.S. =
1
1 cos
2

CHAPTER 14 THE CIRCLE AND ITS PROPERTIES
EXERCISE 62 Page 148
1. If the radius of a circle is 41.3 mm, calculate the circumference of the circle
Circumference, c = 2r = 2(41.3) = 259.5 mm
2. Find the diameter of a circle whose perimeter is 149.8 cm
If per

CHAPTER 13 CARTESIAN AND POLAR CO-ORDINATES
EXERCISE 60 Page 144
1. Express (3, 5) as polar co-ordinates, correct to 2 decimal places, in both degrees and in radians.
From the diagram,
= 5.83
r 3 5
2
and
y
5
tan 1 tan 1
x
3
2
= 59.04 or
59.04
180
rad =

CHAPTER 9 SOLVING EQUATIONS BY ITERATIVE METHODS
EXERCISE 36 Page 83
1. Find the positive root of the equation x + 3x - 5 = 0, correct to 3 significant figures, using the
2
method of bisection.
Let f(x) =
x 3x 5
2
then, using functional notation:
f(0) = -

CHAPTER 6 ARITHMETIC AND GEOMETRIC PROGRESSIONS
EXERCISE 25 Page 52
1. Find the 11th term of the series 8, 14, 20, 26, .
The 11th term of the series 8, 14, 20, 26, is given by:
a + (n 1)d
where
a = 8, n = 11 and d = 6
Hence, the 11th term is: 8 + (11 1)(6

CHAPTER 1 ALGEBRA
EXERCISE 1 Page 4
1. Evaluate 2ab + 3bc - abc when a = 2, b = - 2 and c = 4
When a = 2, b = - 2 and c = 4, 2ab + 3bc - abc = 2(2)(- 2) + 3(- 2)(4) (2)(- 2)(4)
= - 8 24 + 16 = - 16
2. Find the value of 5pq r when p =
2
When p =
2
5
3
, q

EXERCISES PDE 31.10.12-02.11.12
1. Exercise
Let U R be a bounded open set. We say that v C 2 (U ) is subharmonic i v 0 in U .
(a) Prove that subharmonic functions enjoy the following form of the mean-value property: for
every x U , for every r > 0 such th

S CHOOL OF RANDOM DEPARTMENT NAMES
This is the title of the project report
Firstname Lastname
March 15, 2011
1 H EADING ON LEVEL 1 ( SECTION )
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Aenean massa. Cum so

CHAPTER 15 TRIGONOMETRIC WAVEFORMS
EXERCISE 68 Page 163
1. Find all the angles between 0 and 360 whose sine is 0.7321
Sine is negative in the 3rd and 4th quadrants.
sin 1 (0.7321)
= 47.06 as shown in the diagram below.
From the diagram, the two angles bet