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CLS601S - CALCULUS 2 - 1ST OPP - JUNE 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Science; Bachelor of Science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSOC; 07BAMS
LEVEL: 6
COURSE CODE: CLS601S
COURSE NAME: CALCULUS 2
SESSION: JUNE 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
EXAMINER
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
Mr F.N. NDINODIVA, MR. T. KAENANDUNGE
MODERATOR:
Dr S.N. NEOSSI-NGUETCHUE
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
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Question 1 (26 Marks)
Use any appropriate method to find each of the following integrals:
1.1
J —_4—x?_—+_1—12_x—+_9-dx
(e6l
1.2
| ax i
[44]
1.3
[-sec° xsin’x dx
[5]
1.4 ——
[11]
3sinx+4cosx
Questions 2 (28 marks)
2.1. Given f@=x +5x+16, find the x value of the average value on [0, 2].
[8]
2.2
Let
h(©x))=
x
|
dt
t-0
. Find d—dxh.
e5I
2.3 The parametric equation of acurveis y=3t—/?, x=3r". Find the volume generated
when the plain figure bounded by the curve, the x —axis and the ordinates
t=0 and ¢=2, rotates about the x —axis through a complete revolution.
[7]
2.4. Find the area generated when the arc of the parabola y*=8x between
x=0 and x=2, rotates about the x —axis.
[3]
Question 3 (46 Marks)
3.1
Consider
(x)=
1
1
x
3.1.1 Express f(x) as asum of a power series and find the interval of
convergence.
[7]
3.1.2
Use your answer
in 3.1.1 to evaluate
J
ax
l+x°°
[5]
3.2. Find the Maclaurin series of sinx and prove that it represents sinx forall x. [11]
3.3.
Given
the cycloid
x=r(9—sin@),
y =r(1—cos@).
Find
: J2
IX 2
(3]
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3.4 At what points is the tangent in 3.3 vertical?
[5]
3.5
Determine the following polar coordinate in cartesian form:
(V2,—54a).
[5]
3.6
Consider a curve with a polar equation r = 2cos@. Find a cartesian equation for this
curve and state what curve is represented by r =2cos@.
[5]
End of the exai...........cssecseeeee good luck