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CNS512S - CALCULUS FOR NATURAL SCIENCE - 1ST OPP - NOVEMBER 2024 |
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n Am I BI A Unt VE RS ITV
OF SCIEnCEAnDTECHnOLOGY
FacultoyfHealthN, atural
ResourcaensdApplied
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Schoool f NaturalandApplied
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Departmentof Mathematics,
StatisticsandActuariaSl cience
13JacksonKaujeuaStreet
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Windhoek
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T: •264612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION : BACHELOR of SCIENCE
QUALIFICATIONCODE: 07BSOC
COURSE:CALCULUS 1 FOR NATURAL SCIENCE
DATE: NOVEMBER 2024
DURATION: 3 HOURS
LEVEL:5
COURSECODE: CNS512S
SESSION: 1
MARKS: 100
FIRST OPPORTUNITY: EXAMINATION QUESTION PAPER
EXAMINER:
MODERATOR:
INSTRUCTIONS:
Mrs. Hilma Yvonne Nkal/e
Dr. Nega Chere
1. Answer all questions on the separate answer sheet.
2. Pleasewrite 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 = {(1,4), (2,8), (3,12), (4,16), (5,20}.
Question 2 [2 Marks]
= Given f(x) 2x 2 - x + 3, find f(-1).
Question 3 [6 Marks]
Given f(x) = = + 4 and g(x) 2x 2 - 3, find f(g(x)) = 17.
Question 4 [5;4 Marks]
Find the following limits
tanx
(a) lim-.
X---+O X
(b) lim ex-1_
X---+O X
Question 5 [6 Marks]
= Given f(x)
kx 2
{3
is continuous.
if X :5 2
if X > 2
. Find the value of "k" so that the function f
Question 6 [5 Marks]
= = Ify Seas x - 3sin x, prove that cctt2xyz+ y 0.
Question 7 [7 Marks]
Given x = 2at 2 ; y = at 4 . Find ::
Question 8 [5 Marks]
Find the derivative of log(logx), x > 0.
Question 9 [8 Marks]
Let x2 + xy + y 2 = 100 . Find:: by using implicit differentiation.
Question 10 [5 Marks]
Let g be the function defined by g(x) = x3 + x, if f(x) = g- 1 (x) and f(2) = 1, what is the
value of f(2)?
Question 11 [10 Marks]
= Find the stationary points of the function f(x) x3 - 6x 2 + 9x - 2.
Calculus 1 for Natural Science (CNS5125)
15T Opportunity- November 2024
2
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Question 12 [9;5 Marks]
Let f(x) = x(x + 1) 3 • Use detailed sign table in answering the following 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 f: !Rl.\\{2} !Rl.\\{5}defined by f(x) (Sx + 1)/(x - 2) is bijective.
Question 14 [4 Marks]
Given the function below, determine whether it is odd, even or neither. Show your working.
= f(x) 4x 3 - 9
Question 15 [6 Marks]
Given z = f(x,y) = x2y + 2y 4 ex, find af/ ax; af/ ay;(a"2f)/(ax"2)
Calculus 1 for Natural Science (CNS512S)
1srOpportunity- November 2024
3