MAT1512 Latest exam pack questions and answers and summarized notes for exam preparation. Updated for October November 2023 exams . For assistance Whats-App.0.6.7..1.7.1..1.7.3.9 . All the best on your exams!!
Calculus A
Examiners:
First: DR Z.I. ALI
Second: MR S. BLOSE
100 Marks
2 Hours
Closed book and online examination, which you have to write within 2 hours
and submit online through the link: https://myexams.unisa.ac.za/portal
Use of a non-programmable pocket calculator is NOT allowed
This web based examination remains the property of the University of South
Africa and may not be distributed from the Unisa platform.
This examination allows attachment documents only as part of your
submission.
Declaration: I have neither given nor received aid on this examination.
Answer All Questions and Submit within the stipulated timeframe.
Late submission will not be accepted.
This paper consists of 4 pages.
ALL CALCULATIONS MUST BE SHOWN.
[TURN OVER]
, 2 MAT1512
January /February 2023
QUESTION 1
(a) Determine the following limits (if they exist):
x 1 2x 1
(i) lim (3)
x 0 3x 4 2 x 4
(ii) lim
x
x 2
xx (3)
1 cos 3 x
(iii) lim (3)
x sin 2 x
sin 2 x
(iv) lim (2)
x 0 sin 3x
3x 2 6
(v) lim (2)
x 5 2x
(vi) lim
x
25x 2
x 5x (3)
(b) Use the Squeeze Theorem to determine the following limit:
x 2 x sin x
lim (3)
x x 2 cos x
(c) Consider the function f given below:
ax if x 1
f x x 2 a b if 1 x 1
bx if 1 x
(i) Determine the one-sided limits lim f x and lim f x . (2)
x 1 x 1
(ii) Find the one-sided limits lim f x and lim f x . (2)
x 1 x 1
(iii) Hence or otherwise determine the numerical values of a and b . (2)
[25]
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