Pastyear Question Uniten

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COLLEGE OF ENGINEERING
PUTRAJAYA CAMPUS
SEMESTER 1 2010 / 2011
TEST 2
PROGRAMME : Bachelor of Engineering (Honours)
SUBJECT CODE : MATB113
SUBJECT : Advanced Calculus and Analytic Geometry
DATE : 1 October 2010
TIME : 5:15 – 6:15 pm (1 hour)
INSTRUCTIONS TO CANDIDATES:
1. This paper contains THREE (3) questions in ONE(1) page
2. Answer all questions
3. Write all answers in the answer booklet provided
4. Write answer to each question on a new page
THIS QUESTION PAPER CONSISTS OF 2 PRINTED PAGES INCLUDING THIS
COVER PAGE.

2. Page 2 of 2
Question 1 [ marks]
Let C be the curve determined by )(tr kji ttt
etete 
 )cos()sin( for 10  t .
Determine the following:
(a) The length of the curve C .
(b) The tangential component of acceleration Ta at .0t
(c) The normal component of acceleration Na at .0t where
(Hint: Use
2
)(taN v where  )'
)(
1
t
t
T
v
 )
Question 2 [ marks]
(a) Given the function 42
),( yxyxf  and 42
1
),(
yx
yxg

 .
(i) Find the domain of f and g.
(ii) Find
)2,1(),(
lim
yx
),(),( yxgyxf .
(iii) Show that
)0,0(),(
lim
yx
),(),( yxgyxf does not exist.
(b) Identify and sketch the level surface of the function 222
),,( zyxzyxf  that
contains the point )0,0,0( .
Question 3 [ marks]
(a) Show that yxxy zz  for the given yxxez xy 2
ln  .
(b) Suppose ),,( zyxfw  is differentiable at the point )5,24,4( with
,5


x
w
3


y
w
and .7


z
w
If 2
tx  , 3
3ty  and 12  tz , find
dt
dw
at .2t
(Hint: Use the chain rule)
____________________________END OF QUESTIONS-----------------------------------------

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