MTH 1111 Sem I, 2007-08
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INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA END OF SEMESTER EXAMINATION SEMESTER I, 2007/2008 SESSION KULLIYYAH OF ENGINEERING Programme : ENGINEERING Level of Study : UG 1 Time : 9:00 am- 12:00 noon Date : 12/11/2007 Duration : 3 Hrs Course Code : MTH 1112 Section(s) : 1-20 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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CALCULUS 1 MTH 1111FINAL EXAM IIUM SEM 1 07-08
Transcript of MTH 1111 Sem I, 2007-08
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
END OF SEMESTER EXAMINATION SEMESTER I, 2007/2008 SESSION
KULLIYYAH OF ENGINEERING
Programme : ENGINEERING Level of Study : UG 1 Time : 9:00 am- 12:00 noon Date : 12/11/2007 Duration : 3 Hrs Course Code : MTH 1112 Section(s) : 1-20 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) Is it true that a power series may not converge at all ? (3 marks)
(b) Change the improper integral ∫1
0
cos dxxx to an equivalent proper integral. (3 marks)
(c) Find the value of ieπ . (3 marks)
(d) −−−−−−−=⎟⎠⎞
⎜⎝⎛ +
∞→
x
xx
231lim (3 marks)
(e) Determine whether or not xxxf −= cos)( has a zero in [ ]1,0 . Justify. (3 marks) Q2. [15 marks]
(a) Evaluate ii)( . (3 marks)
(b) Evaluate ∫ −1
0
1sin dxx (3 marks)
(c) Write (do not evaluate) the partial fraction decomposition for the function
26
1)(
xxxf
−= (3 marks)
(d) Test for convergence or divergence of ∫−
2
121 dx
x (3 marks)
(e) Evaluate ⎟⎠⎞⎜
⎝⎛ −
∞→x
x1tansinlim (3 marks)
ENGINEERING CALCULUS I MTH 1112
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Q3. [15 marks] (a) Show that the area bounded by 122 =+ yx is equal toπ . (8 marks)
(b) Evaluate dxxx
x∫
−+
+2)223(
62 (7 marks)
Q4. [15 marks]
(a) Find the point on the curve xy cos= closest to the origin. (8 marks)
(b) Determine the Maclaurin’s series of x
xf−
=1
1)( and use it to show that
−−−+−+−=41
31
2112ln (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 scoordinatex − of the local extrema and inflection points of Q6. [8 marks]
At 2=x , discuss continuity and differentiability of 22
24
)(≥<
⎩⎨⎧
=xifxif
xxf
Q7. [8 marks]
Using Simpson’s Rule with 4=n , approximate ∫2
1
1 dxx
.
Q8. [8 marks] Find the volume of the solid obtained by rotating the triangle with vertices
),0()0,(),0,0( randh along .axisy −
Q9. [8 marks]
Find the interval (without testing end points) of convergence for ∑∞
=
−
2 ln4)1(
n
nxnn
nn
Q10. [8 marks]
Evaluate the following; (a) ∫ dxx)sin(ln (4 marks)
(b) ⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛++−
x
xexxdxd
tan
2)ln(ln1sin (4 marks)
