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CLS601S - CALCULUS 2 - 2ND OPP - JANUARY 2024 |
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nAm I BIA UnlVE RS ITY
OF SCIEnCEAnDTECHnDLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: ·264 612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR of SCIENCE
QUALIFICATION CODE: 07BOSC
COURSE: CALCULUS 2
DATE: JANUARY 2024
DURATION: 3 HOURS
LEVEL: 6
COURSE CODE: CLS601S
SESSION: 1
MARKS: 100
SECOND OPPORTUNITY/ SUPPLEMENTARY EXAMINATION: QUESTION PAPER
EXAMINER:
MODERATOR:
Mr. Benson E. Obabueki
Dr. David liyambo
INSTRUCTIONS
1. Answer all questions on the separate answer sheet.
2. Pleasewrite neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the examiner.
4. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
6. Show all your working/calculation steps.
PERMISSIBLE MATERIALS:
1. Non•Programmable Calculator
ATTACHEMENTS
1. None
This paper consists of 2 pages excluding this front page
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Question 1 (28 marks)
1.1 Determine the anti-derivative of x 2 sec2 (x3) using the method of substitution. (6)
1.2 Determine the anti-derivative of (3x+ 4)sin x using integration by parts.
(7)
1.3
Determine
the
anti-derivative
of
-----
(x-
x+2
l)(x
+ 3)
using integration
by partial
fractions.
(7)
1.4
f Determine the integral
using the t-formula.
(8)
smx
Question 2 {18 marks)
2.1 Consider the function f(x) =x4 + 2x 2 + 3. Find the quadratic interpolation polynomial
P2 (x) that interpolates fat the nodes x 0 = -1, x 1 = 0 and x 2 = 1.
(11)
f 2.2 Determine the value of n to estimate the definite integral 1 ex 2 dx within 0.001
0
accuracy using the trapezoidal rule.
(7)
Question 3 {30 marks)
3.1 Determine the area of the region enclosed by the graphs of the functions y =x 2 and
y =-x 2 + 18x.
(8)
3.2 Calculate the length of the first quarter of the circle y 2 + x2 =I.
(10)
3.3 Determine the area of the region generated when the arc of y2 = I 2x between x = I
and x = 3, is rotated completely about the x-axis.
(12)
Question 4 (24 marks)
4.1 Find the volume of the solid formed when the plane figure bounded by y = 5 cos 2x,
the x-axis and ordinates at x =0 and x =f, rotates about the x-axis through a
complete revolution.
(6)
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4.2 Determine the length of the arc of the curve r = cos3 (1) between 0 = 0 and 0 = 37l'.
f0,
d
Use Arclength= r 2 +(_:'.._)2dB
01
dB
(8)
4.3
f2
Given the Maclaurin series cosx = (-1)" x " , write down the first four terms of
n=O
(2n)!
cosx. Hence estimate cos(0.2) using the sixth-degree Maclaurin polynomial. (10)
End of paper
Total marks: 100.
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