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CLS502S - CALCULUS 2 - 1ST OPP - NOV 2022 |
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nAmlBIA UnlVERSITY
OF SCIEnCE AnDTECHnOLOGY
FACULTY OF HEALTH, NATURAL RESOURCES AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Science; Bachelor of Science in Applied iVIathematics and Statistics
QUALIFICATION CODE: 07BOSC; 07BSAM LEVEL:
6
COURSE CODE:
CLS601S
COURSE CODE: CALCULUS2
SESSION:
NOVEMBER 2022 PAPER:
THEORY
DURATION:
3 HOURS
MARKS:
100
FIRST 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.
Find a function f satisfying the following conditions.
J"(x) = 6e2x, f(0) = -3 and J'(0) = 2.
[8]
Question 2.
Evaluate each of the following integrals
[6]
J( b)
2x + 5 sec 2x tan 2x - a~-c;a;2x) dx
[6]
c) f 4 cos x dx
lo 1 + sin2 x
[8]
d) / 3xln2x dx
[6]
e) l[o3 1 dx
[9]
Question 3.
Find the area of the region bounded by the graphs of the equations y = x4 - 2x2 and y = 2x2 .
[10]
Question 4.
In each of the following cases, calculate the volume of the solid generated when the area of the
region bounded by the given curves is revolved around the stated axis.
a) y = sinx, x-axis, x = 0, x = 1r around the y-axis.
[6]
b) y = x2 , x-axis, x = l, x = 3 around the x-axis.
[5]
Question 5.
a) Approximate the following integral using the Trapezoid Rule with n = 4.
lro27sirn 2x dx.
[9]
b) Calculate the arc length of the graph of the function f(x) = ln(secx) on the interval [0, f].
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Question 6.
Determine whether the following series is absolutely convergent, conditionally convergent or
divergent.
[8]
Question 7.
Find the radius and interval of convergence of the following power series.
[9]
END OF EXAMINATION QUESTION PAPER
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