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CLS601S - CALCULUS 2 - 2ND OPP -VJANUARY 2025 |
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i
nAml BIA UnlVERSITY
OF SCIEnCEAnDTECHnOLOGY
FacultoyfHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
Statisticsand ActuarialScience
13JacksonKaujeuaStreet
Private Bag13388
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
DATE: JANUARY2025
DURATION: 3 HOURS
COURSECODE: 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. 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 (29 marks)
Determine the following indefinite integrals using only the indicated method for each:
1.1
f(3t + 5)cos(±)dt using integration by parts.
(6)
1.2
f 3x3
x2 +,7
+4x- -4x
dx usi.ng .integratio. n by part1.al f ract1.ons.
(10)
1.3
f J+ 2 dx using u-substitution. (Hint: Let u =~x-3 ).
(6)
"x-3
f d: 1.4
3 using the t-formula.
(7)
COS- X
Question 2 (18 marks)
2.1
fI
Use the trapezoidal rule to estimate x 3dx with n = 6.
(10)
0
2.2
fI
What value of n will be required to estimate x3dx correct to within 0.001 using
0
the trapezoidal rule?
(8)
Question 3 (10 marks)
3.1 Evaluate the improper integral f.-,-;-dx.
(4)
x-
i
3.2 Calculate the mean value of f(x) = 2,x for Osx s 2.
(6)
3x- +5
Question 4 (19 marks)
4.1 Determine the position of the centroid of the plane figure bounded by y = e2x, the x
-axis, the y-axis and the ordinate x = 2.
(9)
4.2 Determine the length of the first quarter of the circle y 2 + x2 = 1.
(10)
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Question 5 {24 marks)
5.1 Determine up to the fourth-degree term of the Maclaurin's series for f (x) = x2ex
f from the definition. That is, without assuming that e0 = ![:__.
(11)
n! 11;0
5.2 Express (4,60°) in cartesian coordinate form.
(5)
5.3 Determine the equations of the tangent and the normal to the curve
x2 +y 2 - 4.xy+2x =3 at (0 , 2) .
(8)
End of paper
Total marks: 100
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