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CLS601S - CALCULUS 2 - 1ST OPP - NOVEMBER 2023 |
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nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FacultyofHealth,Natural
ResourceasndApplied
Sciences
Schoolof NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
Private Bag13388
Windhoek
NAMIBIA
T: •264 612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR of SCIENCE
QUALIFICATION CODE: 07BOSC
COURSE:CALCULUS 2
DATE: NOVEMBER 2023
DURATION: 3 HOURS
LEVEL:6
COURSECODE: CLS601S
SESSION: 1
MARKS: 100
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY EXAMINATION: QUESTION PAPER
Mr. Benson E Obabueki
Dr. David liyambo
INSTRUCTIONS (add other relevant instructions):
1. Answer all questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the answer script. 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
None
This paper consists of 2 pages excluding this front page
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Question 1 {33 marks)
Determine each of the following indefinite integrals using only the indicated methods. Show
all the working steps.
1.1
f(5x 2 +2)sin2xdx, by parts.
(11)
1.2
f 2x,+I dx, by partial fracti.ons.
x(x· -1)
(9)
1.3
f
2x cos 2xdx, by substitution.
(S)
1.4
f
3
, dx, by trigonometric substitution.
(8)
16-4x·
Question 2 (21 marks)
2.1 Consider the function f (x) =x 3 + 2x 2 + x + I. Find the quadratic interpolation
= = = polynomial P2 (x) that interpolates fat the nodes x0 -1, x 1 0 and x2 1. (11)
2.2 Determine the minimum value of n that will make the Simpson's rule approximation
off3
(x 6 +x 5 +2x+8)dx correct to within an error of 0.001.
(10)
0
Question 3 {35 marks)
3.1 Determine the area of the region enclosed by the graphs of the functions
f(x)=x 2 -4 and g(x)=4-x 2 •
(9)
3.2 Determine the volume of the solid generated when a plane figure bounded by
y=5cos2x, the x-axis, and the ordinates x=0 and x=f ,rotates about the x-axis
through a complete revolution.
(8)
3.3 A plane figure is enclosed by the parabola y2=4x and the line y = 2x. Determine
3.3.1 the position of the centroid of the plane figure.
(12)
3.3.2 the centre of gravity of the solid formed when the plane figure rotates
completely about the x-axis.
(6)
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Question 4 (11 marks)
4.1 Express (-4,3) in polar coordinate form.
4.2 Convert r = sin 20 to rectangular coordinates.
End of paper
(6)
(5)
Total marks: 100.
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