ADDENDUM: Assignments
MAT1512/101/0/2022
ASSIGNMENT 01
Fixed Closing Date: 08 April 2022
Total Marks: 100
1. Determine the following limits:
lim
x2
3 x
6 x 2
and lim
x 2 x 1
3 x 1
Then the correct answers are:
(1) 2 and 2
1
1
(2) and
2
2
(3) 6 and 3
(4) None of the above.
(5)
2.
Determine the following limit:
5x 2 2 x
lim2
2 5x
x
5
Then the correct answer is:
(1) 0
(2) Does not exist
(3) 5
(4) None of the above.
(5)
3.
Determine the following limit:
lim
x
Then the correct answer is:
2
(2) 2
(1)
18
2
sin 2 x 1
sin x 1
MAT1512/101
(3) 1
(4) None of the above.
(5)
4.
Determine the following limit:
lim
x
25 x 2
x x 5
Then the correct answer is:
(1)
(2) 1
(3) Does not exist
(4) None of the above.
(5)
5. Determine the following limit:
lim hx
x4
2x2 8
if
3
where h x
2 x
if
x4
x4
Then the correct answer is:
(1) 2
(2)
8
3
(3) 8
(4) None of the above.
(5)
The following Questions from Question 6, below, to Question 11, below, refer to the function h
below:
Let h be a function defined as:
19
MAT1512/101/0/2022
8 x if x 0
h x x
if 0 x 2
1
x 2 if x 2
2
6.
Determine the following limit:
lim hx
x0
Then the correct answer is:
(1)
(2)
(3)
(4)
7.
0
8
2
None of the above.
(5)
Determine the following limit:
lim h x
x 0
Then the correct answer is:
(1)
(2)
(3)
(4)
8.
0
8
2
None of the above.
(5)
Determine the following limit:
lim hx
x0
Then the correct answer is:
(1)
(2)
(3)
(4)
9.
0
8
Does not exist.
None of the above.
(5)
Determine the following limit:
lim hx
x2
Then the correct answer is:
(1)
(2)
(3)
(4)
20
2
8
6
None of the above.
(5)
MAT1512/001
10. Determine the following limit:
lim hx
x2
Then the correct answer is:
(1)
(2)
(3)
(4)
2
8
6
None of the above.
(5)
11. Determine if the function h is continuous at x 0 and x 2 .
Then the correct answer is:
(1)
(2)
(3)
(4)
Yes, the function h is continuous at both x 0 and x 2 .
No, the function h is NOT continuous at both x 0 and x 2 .
The function h is NOT continuous at x 0 but is continuous at x 2 .
None of the above.
(5)
The following Questions from Question 12, below, up to and including Question 18, below,
are about finding Limits from a graph.
Let the graph of the particular function g x be represented as shown below (the graph is
NOT drawn to scale):
Use the graph of g in the figure above to find the following values, if they exist:
21
MAT1512/101/0/2022
12.
g 2
Then the correct answer is:
13.
(1) 1
(2) 3
(3) Undefined.
(4) None of the above.
(5)
(4) None of the above.
(5)
lim g x
x 2
Then the correct answer is:
(1) 2
(2) 1
(3) Undefined.
(4) None of the above.
(5)
14. lim g x
x 2
Then the correct answer is:
(1)
-2
(2)
-3
(3)
-1
(4)
None of the above.
(5)
15. lim g x
x 2
Then the correct answer is:
(1) 1
(2) 2
(3) 3
(4)
(5)
22
None
of
the
above.
MAT1512/001/01/2022
16.
lim g x
x 2
Then the correct answer is:
(1) 2
(2) 3
(3) 1
(4) None of the above.
(5)
17.
lim g x
x 2
Then the correct answer is:
(1) 1
(2) 2
(3) 3
(4) None of the above.
(5)
18. Identify the discontinuities in the function g x graphed above.
Then the correct answer is:
(1) x 2 , removable discontinuity and x 2 , Jump discontinuity.
(2) x 3 , essential discontinuity and x 2 , jump discontinuity.
(3) x 2 , Jump discontinuity and x 2 , removable discontinuity.
(4) None of the above.
19. Use the squeeze Theorem to determine
lim
x
(5)
3 sin e x
x2 2
Then the correct answer is:
(1) 0
(2)
4
2
(3)
2
2
23
MAT1512/101/0/2022
(5)
(4) None of the above.
20. Let
2
sin x 2 4
x
1
x2 4
f x b
a cos x 2
if
x2
if
x2
if
x2
Determine the values of a and b that make the function f x continuous at x 2 .
Then the correct answers are:
(1) a 2 and b 5
(2) a 5 and b 2
(3) a 5 and b 5
(4) None of the above.
(5)
GRAND TOTAL: [100]
24
0
