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CNS512S - CALCULUS FOR NATURAL SCIENCE - 2ND OPP - JANUARY 2025 |
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f
nAml BIA UnlVERSITY
OF SCIEnCEAnDTECHnOLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
Statisticsand ActuarialScience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: •264 612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR of SCIENCE
QUALIFICATIONCODE: 07BSOC
COURSE:CALCULUS 1 FOR NATURAL SCIENCE
DATE: JANUARY 2025
DURATION: 3 HOURS
LEVEL:5
COURSECODE: CNS512S
SESSION: 2
MARKS: 100
SECOND OPPORTUNITY/SUPPLEMENTARY: EXAMINATION PAPER
EXAMINER:
MODERATOR:
INSTRUCTIONS:
Mrs. Hilma Yvonne Nkalle
Dr. Nega Chere
1. Answer all questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the examiner.
4. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator
This paper consists of 3 pages including this front page
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Question 1 [2 Marks]
Find the domain and the range of the given relation.
R = {(1,7), (5,3), (7,9), (-2, -3), (-2,8}.
Question 2 [2 Marks]
Given g(x) = -3x - 2, find g(2).
Question 3 [6 Marks]
Given f(x) = ex and g(x) = 4x 3 + 7, find g(f(x)) = 18.
Question 4 [5;4 Marks]
Find the following limits
3x 5 + x2 -1
+ (a) lim
X---+C
X2
5
.
Question 5 [6 Marks]
Given f(x)
=
{~x-:_
1
5
continuous.
ifx 5
ifx > 5
Question 6 [5 Marks]
Given y = cos- 1 (x), find :~-
. Find the value of "k" so that the function f is
Question 7 [7 Marks]
Given x = acos0; y = bcos0. Find:~-
Question 8 [5 Marks]
Find the derivative of cos (logx + ex), x > 0.
Question 9 [8 Marks]
Let 2x + 3y = siny. Find :~ by using implicit differentiation.
Question 10 [5 Marks]
Let f(x) = ~x 3 + x - = 1. What is the value of (f- 1)' (x) when x 3?
4
Question 11 [10 Marks]
Find the stationary points of the function f(x) = x3 - x2 - 3x + 2.
3
Calculus 1 for Natural Science (CNS512S)
2NDOpportunity- JANUARY 2025
2
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Question 12 [9;5 Marks]
= Let f(x) ~x 3 + x 2 - 15x - 9. Use detailed sign table in answering the following
3
questions.
(a) Find the intervals in which f is increasing or decreasing.
= (b) Find the intervals in which the graph of y f(x) is concave upward or downward.
Question 13 [11 Marks]
Prove that the function g: !Rl.\\{1}
= !Rl.\\{O}defined by f(x) (2x + 3)/(x + 1) is bijective.
Question 14 [4 Marks]
Given the function below, determine whether it is odd, even or neither. Show your working.
xz
f(x) =- x3- -x
Question 15 [6 Marks]
Given f(x, y, z) = xcosz + x 2y 3 ez, find af/ ax; af/ ay; (af)/(az)
Calculus 1 for Natural Science {CNS512S)
2N°opportunity- JANUARY 2025
3