MTH 1111 Sem II, 2007-08
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INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA END OF SEMESTER EXAMINATION SEMESTER II, 2007/2008 SESSION KULLIYYAH OF ENGINEERING Programme : ENGINEERING Level of Study : UG 1 Time : 2:30 pm- 5:30 pm Date : 31/3/2008 Duration : 3 Hrs Course Code : MTH 1112 Section(s) : 1-10 Course Title : ENGINEERING CALCULUS I This Question Paper Consists of Four (4) Printed Pages (Including Cover Page) With Ten (10) Questions. INSTRUCTION(S) TO CANDIDATES DO NOT OPEN UNTIL YOU ARE ASKED TO DO SO • This question paper consists of two sections, for specific instructions; please refer to the appropriate section. • Answers should be clear and intelligible. • Justify your answer with simplification of intermediate steps for full marks. • No book, notes and programmable calculator are permitted Any form of cheating or attempt to cheat is a serious offence which may lead to dismissal.
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MTH 1111 CALCULUS 1 FINAL EXAM IIUMSEM 2 0708
Transcript of MTH 1111 Sem II, 2007-08
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
END OF SEMESTER EXAMINATION SEMESTER II, 2007/2008 SESSION
KULLIYYAH OF ENGINEERING
Programme : ENGINEERING Level of Study : UG 1 Time : 2:30 pm- 5:30 pm Date : 31/3/2008 Duration : 3 Hrs Course Code : MTH 1112 Section(s) : 1-10 Course Title : ENGINEERING CALCULUS I This Question Paper Consists of Four (4) Printed Pages (Including Cover Page) With Ten (10) Questions.
INSTRUCTION(S) TO CANDIDATES DO NOT OPEN UNTIL YOU ARE ASKED TO DO SO
• This question paper consists of two sections, for specific instructions; please refer to the appropriate section.
• Answers should be clear and intelligible. • Justify your answer with simplification of intermediate steps for full marks. • No book, notes and programmable calculator are permitted
Any form of cheating or attempt to cheat is a serious offence which may lead to dismissal.
ENGINEERING CALCULUS I MTH 1112
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Section A [60 marks] [Answer all questions of this section]
Q1. [15 marks]
(a) Find )3(1−f if 1)( 3 += xxf . (5 marks)
(b) Discuss the continuity and the differentiability of ⎩⎨⎧
>
≤=
0,
0,sin)( 2 xx
xxxf at 0=x .
(5 marks)
(c) Find dxdy of 21 1sin xy −= − . (5 marks)
Q2. [15 marks]
(a) Write i−3
12 in the form iba + and then convert it into polar form. (5 marks)
(b) Evaluate ∫ − dxxx 1tan . (5 marks)
(c) Find the total area bounded by xxy 22 −= and −x axis on ]3,0[ . (5 marks) Q3. [15 marks] (a) Sketch the region R that is bounded by the graph of 682)( 2 −+−= xxxf and
62)( −= xxg . Find the volume of the solid generated by revolving R about y-axis. (8 marks)
(b) Evaluate dxxx
xxx∫ +−
++−44
19822
23 (7 marks)
ENGINEERING CALCULUS I MTH 1112
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Q4. [15 marks]
(a) Evaluate dxx
x∫
+ 42
2 (8 marks)
(b) Determine Maclaurin series of x
xf−
=11)( and then use it to find Maclaurin series
for xxf 1sin)( −= . (7 marks)
ENGINEERING CALCULUS I MTH 1112
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Section B [40 marks] [Answer only Five (5) questions]
Q5. [8 marks]
Find the ⎥⎦
⎤⎢⎣
⎡−
+→ xxx
1)1ln(
1lim0
.
Q6. [8 marks]
Determine the radius of convergence of the series ∑∞
=1
2
)!2()!(
n
n
nxn
.
Q7. [8 marks]
Determine the position function if the velocity function is tetv t 2sin)( = and the initial position is 0)0( =s .
Q8. [8 marks]
At noon, Ship A is km190 west of ship B . Ship A is sailing east at hkm /35 and ship B is sailing north at hkm /25 . How fast is the distance between the ships changing at 00:4 P.M.?
Q9. [8 marks]
Find dxdy
if xxy 4sin)(cos= .
Q10. [8 marks]
Test for convergence or divergence of dxx∫1
0
2)(ln .
