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CLS502S - CALCULUS 1 - 2ND OPP - JAN 2023 |
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(
I
nAmtBIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF HEALTH, NATURAL RESOURCES AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Science; Bachelor of Science in Applied lVIathematics and Statistics
QUALIFICATION CODE: 07BOSC; 07BSAM LEVEL:
5
COURSE CODE:
CLS502S
COURSE CODE: CALCULUS I
SESSION:
JANUARY 2023 PAPER:
THEORY
DURATION:
3 HOURS
MARKS:
100
SUPPLEMENTARY/
EXAMINER:
MODERATOR:
SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
DR. DSI IIYAMBO
DR. N CHERE
INSTRUCTIONS
l. 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 2 PAGES (Including this front page)
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Question 1.
Consider the functions f(x) = 4x2 + 9, g(x) =~and
h(x) = 4x 2 - 3; x 0.
Y- 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.)
11. 111
4x + 12
x 3 + 3x 2 - 4x -
12 .
[5]
{ii) lim (ex+ x)xI
[8]
b) Use the c - 8 method to show that lim (lOx - 6) = 14.
[7]
Question 3.
a) Use the definition
(first principle)
to find the derivative of f(x)
l
= 27f
-
x-
X+
1l 22 .
[10]
b) Differentiate the function f(x) = (ln3)secx + tan- 1(ln4x).
[6]
c) If the equation x 2y+siny = 2n determines 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, 2n).
[8]
Question 4.
Let f (x) = I2x - 10I+ 2 .
a) Show that f is continuous at x = 5.
[7]
b) Show that f is not differentiable at x = 5.
[8]
Question 5.
Let f(x)
x4
=4
- 2x2 + 4 and g(x) = 2x4 -
8x 3 + 3l6x -
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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