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CLS601S - CALCULUS 2 - 1ST OPP -NOVEMBER 2024 |
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nAml BIA UnlVERSITY
OF SCIEnCE AnDTECHnOLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
p
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: •264 61207 2913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR of SCIENCE IN APPLIED MATHEMATICS AND STATISTICS and
BACHELOR OF SCIENCE
QUALIFICATIONCODE: 07BSAM / 07BOSC
LEVEL:6
COURSE:CALCULUS 2
COURSECODE: CLS601S
DATE: NOVEMBER 2024
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY: EXAMINATION QUESTION PAPER
Mr Benson.E Obabueki
Dr. David liyambo
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 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. All written work must be done in blue or black ink and sketches in pencil.
7. Show clearly all the steps used in the calculations.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator without a cover.
ATTACHEMENTS
None
This paper consists of 2 pages excluding this front page
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Question 1 (28 marks)
Determine the following indefinite integrals using only the indicated method for each:
1.1
f(w+4)sin(5w)dw using integration by parts.
(6)
1.2
f 3x+ 7
X 2 -x-6
dx us.ing .integratio. n by parti.a If racti.ons.
(8)
1.3
f .J dx us.ing tng. onometnc. substi.tutio. n.
98-2x 2
(7)
f :~x 1.4
using the t-formula.
(7)
sm-x
Question 2 (19 marks)
2.1
fI
Use the midpoint rule to estimate (x 3 + x 2 )dx with n = 6.
(10)
0
2.2
fI
What value of n will be required to estimate (x 3 + x 2 )dx correct to within 0.001
0
using the midpoint rule.
(9)
Question 3 (20 marks)
3.1
J3
Evaluate the improper integral
dx if it is convergent.
(10)
0 -v3-x
3.2 Calculate the root mean square value of f(x) =--2 for O::;x::; 2.
(10)
x+3
Question 4 (19 marks)
4.1 Determine the volume of the solid generated when a plane figure bounded by
t y =5cos 2x, the x-axis, and the ordinates x =0 and x = ,rotates about the x-axis
through a complete revolution.
(7)
4.2 A curve is defined by the parametric equations x = 0-sin 0 and y = 1-cos 0.
Determine the area of the surface generated by the curve between 0 = 0 and 0 = 21r,
when rotated completely about the x-axis.
(12)
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Question 5 (14 marks}
5.1 Determine the Taylor's series for f(x) = e-x about x = 2 from the definition. That is,
=I-. without assuming that e0 "'0"
(9)
n=O n!
5.2 Express (-4,3) in polar coordinate form.
(5)
End of paper
Total marks 100%
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