Mat235 2012 Okt
Mat235 2012 Okt
Mat235 2012 Okt
CS/OCT 2012/MAT235/241/243
COURSE
COURSE CODE
MAT235/241/243
EXAMINATION
OCTOBER 2012
TIME
2 HOURS
INSTRUCTIONS TO CANDIDATES
1.
2.
Answer ALL questions in the Answer Booklet. Start each answer on a new page.
3.
Do not bring any material into the examination room unless permission is given by the
invigilator.
4.
Please check to make sure that this examination pack consists of:
i)
ii)
CONFIDENTIAL
CONFIDENTIAL
CS/OCT 2012/MAT235/241/243
QUESTION 1
a)
b)
If z = (2x - 3) 2 e y , x =
v
_J_
c)
Given
x +3
(x - 1 ) ( X
+ 1)
Bx + C
+
x -1
x2 + 1
QUESTION 2
a)
b)
2
Given a function f(x, y) = y 3 - 2xy - 12y + x 2
i) Find all the critical points of the function.
(5/4 marks)
ii) Determine the relative maximum, relative minimum and saddle point(s), if any.
(2Y2 marks)
CONFIDENTIAL
CONFIDENTIAL
CS/OCT 2012/MAT235/241/243
QUESTION 3
a)
Evaluate
-dx
J ( x 2 + 2)3
0
b)
(5 marks)
Find the general solution of the first order linear differential equation
dy
. 2
x ^ L + y = sin x.
dx
(5 marks)
c)
Evaluate I ,
J V x 2 - 16
QUESTION 4
a)
b)
dy
iv
+ x.
(8 marks)
CONFIDENTIAL