 |
CLS502S - CALCULUS 1 - 1ST OPP - JUNE 2022 |
|
|
1 Page 1 |
▲back to top |
o
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
ee
SESSION: JUNE 2022
DURATION: 3 HOURS
LEVEL: 5
COURSE NAME: CALCULUS 1
PAPER: THEORY
MARKS: 100
EXAMINER
MODERATOR:
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
Mrs. H. Y. Nkalle
Dr.v. NBl.. Ch Shere
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
Show clearly all the steps used in the calculations.
3. 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)
1|Paege
|
|
2 Page 2 |
▲back to top |
Question 1
Consider the relation P = {(1,7), (—1,7), (3,9), (1,3)}. Is P a function? Justify your answer.
[2]
Question 2
Show that lim 2 = 0,
[6]
x-0
x
Question 3
Find xliam ea V3a+x—2Vx °
[8]
Question 4
Find the average rate of change of the function f(x) = x” + 4x over the interval [-6, 4]. [5]
Question 5
Find the instantaneous rate of change at x = b for the function f(x) = x? + 2x.
[5]
Question 6
Consider the function f(x) = e’* . Determine the values ofr so thatf satisfies the
equation f'"(x) + f'(x) — 6f(x) = 0.
[8]
Question 7
Find the equation of the tangent line to the graph of the function f(x) = Vx at the point
(1,1).
[5]
Question 8
Differentiate f(x) = — from first principle.
[7]
Question 9
Let f(x) = c. Find f'(x) using limit definition of derivative.
[3]
Question 10
Find the range of f(x) = V1 — x?.
[5]
Question 11
Let f(z) = Inz. Find f’"(z)/z = 2.
[4]
2|Page
|
|
3 Page 3 |
▲back to top |
Question 12
Find = by using implicit differentiation of xy = 1.
[4]
Question 13
Use logarithmic differentiation to find = (x¥8),
[5]
Question 14
Investigate whether the following functions are odd or even.
(a) f= x,
[2]
(b) f(x) = cosx.
[2]
Question 15
Let f(x) = =x3 + x? —15x — 9. Use detailed sign tables 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.
[6]
Question 16
Air is escaping from a spherical balloon at the rate of 2cm? per minute. How fast is the
radius shrinking when the volume is 361 cm? ?
[8]
Question 17
Find the rate of change of the area A, of the circle with respect to its circumference
CiLe e S7
[6]
3|Page
End of paper
Total marks:100