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CLS502S - CALCULUS 1 - 2ND OPP - JULY 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES & NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Science; Bachelor of Science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSOC; 07BAMS
LEVEL: 5
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COURSE NAME: CALCULUS 1
SESSION: JULY 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SUPPLEMENTARY/ SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
Mrs. H. Y. Nkalle
MODERATOR:
Dr. N. Chere
INSTRUCTIONS
Answer ALL the questions in the booklet provided.
Show clearly all the steps used in the calculations.
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
Consider the relation R = {(1,9), (2,7), (1,4)}. Is R a function? Justify your
answer.
[2]
Question 2
Let f(x) = ——. Use a detailed sign table to find the domain of f. [8]
Question 3
Find lim 2+.
x 93 0 «X-3
[7]
Question 4
Differentiate f(x) = a from first principle.
[7]
Question 5
Prove that f(x) = 3x +5 is injective.
[4]
Question 6
Investigate whether the following functions are odd or even.
(a) f(x) = x’.
[2]
(b) f(x) = sinx.
[2]
Question 7
Show that tan x = sec*x using quotient rule.
[3]
Question 8
Let f(x) = x(x + 1). Use detailed sign table in answering the following questions.
(a) Find the intervals in which f is increasing or decreasing.
[9]
(b) Find the intervals in which the graph ofy = f (x) is concave upward or downward.
[5]
Question 9
Let f(x) =
3x+3cifx22
x*—cxifx<2
. Af lim f (x) exists, find the values of c.
x-
[6]
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Question 10
Find the point on the graph of the function f(p) = 3p” — p + 1 at which the tangent line is
horizontal.
[12]
Question 11
Consider the function f(x) = e’*. Determine the values of r so that f satisfies the equations
F'() — 3f"(&) + 2f'"(x) = 0.
[9]
Question 12
Given f(x,y) = xcosy? + In(1+ xy). Find fy, fix fy and fyr.
[7]
Question 13
Find limae
[8]
Question 14
Find the average rate of change of the function f(x) = x? + 4x over the interval [—6; 9].
[4]
End of paper
Total marks: 100
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