1
Cork Institute of Technology
Bachelor of Engineering in Mechanical Engineering โ Stage 2
(EMECH_7_Y2)
Autumn 2008
Mathematics
(Time: 3 Hours)
Answer FIVE questions Examiners: Ms. J. English
Dr. D. Cremin
Mr. A. Bateman
Dr. P. Delassus
Q1. (a) A curve is described by the parametric equations 12
13
t
xt
โ
=
+
,13
12
t
yt
โ
=+
Find the value of dy
dx when t = 2. [7 marks]
(b) If 34 2
448xy xyโโ = , find dy
dx at the point (1, 4). [6 marks]
(c) Show that the equation x3+4x =1 has a root between x = 0 and x = 1 .Use the
Newton-Raphson method with three iterations to find the root correct to two
decimal places.
[7 marks]
Q2. (a) Given n = -7x3 +5x2y3+6y find
,
nn
x
y
โโ
โโ
and
2
2
n
y
โ
โ [6 marks]
(b) You are given that
4
2
5kN d
Rb
= where k is a constant and d, N and b are variables.
Use a calculus method to find the approximate percentage error in R due to errors of
+2.5% in d, 3% in N and โ3.2% in b.
[8 marks]
(c) Locate the turning points on the curve
32
18 9 26
63
nn
sn
=
โโ+ and establish
whether they are maximum or minimum points. [6 marks]
