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CLS601S - CALCULUS 2 - 2ND OPP - JULY 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: JULY 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SUPPLEMENTARY/SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
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 (20 Marks)
Use any appropriate method to find each of the following integrals:
1.1
[ cosea sin
[4]
1.2 fsin? xdx
(4]
1.3 fin x de
[4]
1.4 i} sin? (2x) cos(3x)dx
[3]
Questions 2 (35 marks)
2.1 Considera function f(x) =x* —6x, x€[0,3].
2.1.1 Use the fundamental theorem of calculus to evaluate the integral of the
function over the given interval.
[3]
2.1.2 Evaluate the Riemann sum for the function taking sample points to be right
end points with 7 subintervals.
[10]
2.2
={"
di
[5]
dx
2.3
Find the area of the region enclosed by f(x) = 41 x° +, 12x+9 on [0,3].
[8]
2.4 Determine the length of the curve x =2cos*@, y=2sin*>@ between the point
corresponding to 6 = Oand O=5:
[9]
Question 3 (45 Marks)
3.1
Consider f(x)= l+x1
3.1.1 Express f(x) as a sum of a power series and find the interval of
convergence.
[7]
3.1.2 Use your answer in 3.1.1 to evaluate p1=+x°
[5]
3.2
Find the Maclaurin series of cosx and prove that it represents cosx forall x. [11]
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3.3
Approximate the function f(x) = Vx by a Tylor polynomial of degree 2 centered-
at 4.
[5]
3.4
Find the equation of the tangent to the cycloid x =r(@-sin9@), y=r(1—cos@) at the
point where O=7.
[7]
3.5 At what points is the tangent in 3.4 horizontal?
[4]
3.6
Determine the following cartesian coordinate in polar form:
(-2,-2).
[6]
End of the exai............sssccseees ....g00d luck