 |
CLS502S - CALCULUS 1 - 1ST OPP - NOVEMBER 2023 |
|
|
1 Page 1 |
▲back to top |
nAmlBIA UnlVERSITY
OF SCIEnCE AnDTECHnOLOGY
Facultyof Health,Natural
ResourceasndApplied
Sciences
Schoolof Natural and Applied
Sciences
Department of Mathematics,
<;t;iti<.tir<. ;inrl Artu;iri;il <;riPnrP
13Jackson Kaujeua Street
PrlvJte 8.1,:13388
Windhoek
NAMIBIA
T: •254 61 207 2913
E: ms.1s@nust.na
W: www.nust.nJ
QUALIFICATION:BACHELOROF SCIENCEIN APPLIEDMATHEMATICSAND STATISTICS
QUALIFICATIONCODE:
07BSAM
LEVEL:
5
COURSE:
CALCULUS1
COURSECODE:
CLS502S
DATE:
NOVEMBER2023
SESSION:
1
DURATION:
3 HOURS
MARKS:
100
FIRSTOPPORTUNITYEXAMINATION:QUESTIONPAPER
EXAMINER:
MODERATOR:
Dr. David liyambo and Mrs. Yvonne Nkafle
Dr. Nega Chere
INSTRUCTIONS(add other relevant instructions):
1. Attempt all the questions in the booklet provided.
2. Please write neatly and legibly using a black or blue inked pen, and sketches must be done in
pencil.
3. Do not use the left side margin of the answer script. This must be allowed for the examiner.
4. No books, notes or other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
6. Show clearly all the steps used in the calculations.
PERMISSIBLEMATERIALS:
1. Non-programmable calculator without a cover.
ATTACHMENTS:
None
This paper consistsof 3 pages includingthis front page
|
|
2 Page 2 |
▲back to top |
Question 1.
Consider the functions f(x) = 4x 2 + 9, g(x) = Jl - x 2 and h(x) = 4x 2 - 3; x 2: O.
7" 1.1 Find the sum of the smallest and the largest numbers in the domain of
[S]
1.2 Determine whether g is even, odd or neither.
[3]
1.3 Determine whether h- 1 exists. If it does, find it.
[9]
Question 2.
2.1 Find the following limits, if they exist.
a) I.,m
x-t-3
4x + 12
x 3 + 3x-? - 4x -
•
12
(4]
b) lim (ex+ x):1.
[7]
x-to+
= 2.2 Use thee - 8 method to show that lim (lOx - 6) 14.
(7]
x-t2
Question 3.
Let f (x) = I2x - 10I + 2 .
3.1 Show that f is continuous at x = 5.
[7]
3.2 Show that f is not differentiable at x = 5.
[8]
Question 4.
=-;-- 4.1 Use the definition (first principle) to find the derivative of f(x)
1r-
Xx+-
~-
2
[7]
4.2 Differentiate each of the following functions
= a) f(x) (ln3)secx +tan- 1(In4x).
[S]
b) g(x) = (2x3 + 5)h 2 +7
[7]
Question 5.
= = 5.1 If the equation x 2y + sin y 21r determines a differentiable function f such that y f(x), find
the slope of the tangent line to the graph of this equation at the point P(l, 21r).
[6]
5.2 Without finding the inverse function 1- 1, find (f- 1)'(b), where f (x) = e2x- 5 and b = f(-10).
[7]
1
|
|
3 Page 3 |
▲back to top |
Question 6.
Let f(x)
=
x4.
4
- 2x 2 + 4 and g(x) =
2x4 -
8x3 + 316x -
172.
6.1 Find the intervals on which f is increasing and on which it is decreasing.
[9]
6.2 Find the intervals on which the graph of y = g(x) is concave upwards and on which it is concave
downwards.
[9)
2