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CLS502S - CALCULUS 1 - 1ST OPP - NOVEMBER 2024 |
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nAm I BIA UnlVERSITY
OF SCIEnCE AnOTECHnOLOGY
Facultyof Health,Natural
ResourcesandApplied
Sciences
School of Natural and Applied
Sciences
Department of Mathematics,
<;t;iti,tir<. ;inrl Artu;iri;il <;riPnrP
13Jackson Kaujeua Street
Private Bag 13388
Windhoek
NAMIBIA
T: •264 61 207 2913
E: msas@nust.na
W: www.nust.n,1
QUALIFICATION:BACHELOROF SCIENCEIN APPLIEDMATHEMATICSAND STATISTICS& BACHELOROF SCIENCE
QUALIFICATIONCODE:
07BSAM, & 07BSOC
LEVEL:
5
COURSE:
CALCULUS 1
COURSECODE:
CLS502S
DATE:
NOVEMBER 2024
SESSION:
1
DURATION:
3 HOURS
MARKS:
100
FIRST OPPORTUNITY EXAMINATION: QUESTION PAPER
EXAMINER:
MODERATOR:
Dr. David liyambo
Dr. Nega Chere
INSTRUCTIONS:
1. Attempt all the questions in the booklet provided.
2. Please write neatly and legibly using a black or blue inked pen, and sketches must be done in
pencil.
3. Do not use the left side margin of the answer script. This must be allowed for the examiner.
4. No books, notes or other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
6. Show clearly all the steps used in the calculations.
PERMISSIBLE MATERIALS:
1. Non-programmable calculator without a cover.
ATTACHMENTS:
None
This paper consists of 2 pages including this front page
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Question 1.
Consider the functions f(x) = 4x 2 + 9, g(x) =~and
h(x) = 4x 2 - 3; x 0.
7" a) Find the sum of the smallest and the largest numbers in the domain of
[9]
b) Determine whether g is even, odd or neither.
[4]
c) Determine whether h- 1 exists. If it does, find it.
[10]
Question 2.
a) Find the following limits, if they exist.
+ (I')
1I. m
·
x3
4x + 12
3x2 - 4x -
.
12
[SJ
(ii) lim (ex+ x)x1
[8]
b) Use the£ - 6 method to show that lim (lOx - 6) = 14.
[7]
Question 3.
a)
Use the definition (first principle) to find the derivative
of f(x)
=
1
2
7f
-
x-1
X+
v'2
2
[10]
b) Differentiate the function f(x) = (In 3)secx + tan- 1(1n4x).
[6]
c) If the equation x2 y + sin y = 27rdetermines a differentiable function f such that y = f (x), find the
equation of the tangent line to the graph of the given equation at the point P(l, 27r).
[8]
Question 4.
Let f (x) = I2x - 10 I+ 2 .
a) Show that f is continuous at x = 5.
[7]
b) Show that f is not differentiable at x = 5.
[8]
Question S.
Let f(x)
=
x4
4
- 2x 2 + 4 and g(x) = 2x4 -
8x3 + 316x -
172.
a) Find the intervals on which f is increasing and on which it is decreasing.
[9]
b) Find the intervals on which the graph of y = g(x) is concave upwards and on which it is concave
downwards.
[9]
END OF EXAMINATION QUESTION PAPER
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