MAT1512
Exam Papers Bundle
2010-2022
Past Question Papers
Contains Questions ONLY
,MAT1512
Exam Papers Bundle
2010-2022
Past Question Papers
Contains Questions ONLY
, 1 MAT1512
January /February 2022
UNIVERSITY EXAMINATIONS
January/February 2022
MAT1512
Calculus A
Examiners:
First: DR S.B. MUGISHA
Second: DR Z. ALI
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 2022
QUESTION 1
(a) Determine the following limits (if they exist):
6 x 2
(i) lim (3)
x2 3 x 1
x3
(ii) lim (3)
x 3 x2 9
x2 4x 2x
(iii) lim (3)
x 2x
1 x
(iv) lim (3)
x 1 1 x
2x
(v) lim (3)
x 0 3 x9
sin t tan 2t
(vi) lim (3)
t 0 t
(b) Use the Squeeze Theorem to determine the following limit:
5k 2 cos 3k
lim . (3)
k k 2 10
x 2 if x2
(c) Let G ( x)
x 2 if x2
(i) Draw the graph of G x . (1)
(ii) Determine lim G ( x) . (2)
x 2
(iii) Is G x continuous at x 2 ? Give a reason for your answer. (1)
[25]
QUESTION 2
(a) By the first principles of differentiation, find the derivative of f x 2 x 2 3x 4
at x 2 . (5)
(b) Find the derivatives of the following functions by using the appropriate rules of
differentiation:
x2 x
(i) f x (3)
sin x cos x
g x cos 5x
sin x 2
(ii) (3)
Exam Papers Bundle
2010-2022
Past Question Papers
Contains Questions ONLY
,MAT1512
Exam Papers Bundle
2010-2022
Past Question Papers
Contains Questions ONLY
, 1 MAT1512
January /February 2022
UNIVERSITY EXAMINATIONS
January/February 2022
MAT1512
Calculus A
Examiners:
First: DR S.B. MUGISHA
Second: DR Z. ALI
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 2022
QUESTION 1
(a) Determine the following limits (if they exist):
6 x 2
(i) lim (3)
x2 3 x 1
x3
(ii) lim (3)
x 3 x2 9
x2 4x 2x
(iii) lim (3)
x 2x
1 x
(iv) lim (3)
x 1 1 x
2x
(v) lim (3)
x 0 3 x9
sin t tan 2t
(vi) lim (3)
t 0 t
(b) Use the Squeeze Theorem to determine the following limit:
5k 2 cos 3k
lim . (3)
k k 2 10
x 2 if x2
(c) Let G ( x)
x 2 if x2
(i) Draw the graph of G x . (1)
(ii) Determine lim G ( x) . (2)
x 2
(iii) Is G x continuous at x 2 ? Give a reason for your answer. (1)
[25]
QUESTION 2
(a) By the first principles of differentiation, find the derivative of f x 2 x 2 3x 4
at x 2 . (5)
(b) Find the derivatives of the following functions by using the appropriate rules of
differentiation:
x2 x
(i) f x (3)
sin x cos x
g x cos 5x
sin x 2
(ii) (3)
