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CLS601S - CALCULUS 2 - 1ST OPP - JAN 2023 |
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nAmlBIA untVERSITY
OF SCIEnCEAnDTECHnOLOGY
FACULTY OF HEALTH, NATURAL RESOURCES AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Science; Bachelor of Science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BOSC; 07BSANI LEVEL:
6
COURSE CODE:
CLS601S
COURSE CODE: CALCULUS2
SESSION:
JANUARY 2023 PAPER:
THEORY
DURATION:
3 HOURS
MARKS:
100
SUPPLEMENTARY / SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER:
DR. DSI IIYAMBO
MODERATOR:
DR. N CHERE
INSTRUCTIONS
1. Attempt 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 black or blue inked, 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.
Consider the function f(x) = 3x, on the interval [O,10]. Using the left-hand end point of each
subinterval and n = 10, calculate the Riemann sum of f
[8]
Question 2.
Eva!uate each of the following integrals
a) / ( 1 - ~) cos (x - ln x) dx
[7]
b)
3
l{o
1
J3=x
dx
[9]
Jc) J4 - x2 dx
[12]
lfx d)
ecosx sin(2x) dx.
[13]
Question 3.
Approximate the following integral using the Trapezoid Rule with n = 4.
{2-;r
lo sin 2x dx
[9]
Question 4.
Determine the volume of the solid obtained by rotating the portion of the region bounded by
y = ijx and y = that lies in the first quadrant, about the y-axis, using the disk method.
[9]
Question 5.
Use the Simpson's rule with n = 4 to approximate the arclength of the graph of y = x2 + x + 3
from A(-2, 5) to B(2, 9).
[12]
Question 6.
Find the nth partial sum of the following series, and hence determine the sum of the series, if it
converges.
(1 1) 00
I: 3i - 3i+l
i=l
[9]
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Question 7.
Find the radius and interval of convergence of the following power series.
oo
n
I: 4:vn
n=l
[12]
END OF EXAMINATION QUESTION PAPER
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