# MAT1512 TL101 0 2022 Assignment1

```ADDENDUM: Assignments
MAT1512/101/0/2022
ASSIGNMENT 01
Fixed Closing Date: 08 April 2022
Total Marks: 100
1. Determine the following limits:
lim
x2
3 x
6 x 2
and lim
x   2 x  1
3  x 1
(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
(1) 0
(2) Does not exist
(3) 5
(4) None of the above.
(5)
3.
Determine the following limit:
lim
x

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
(1)  
(2) 1
(3) Does not exist
(4) None of the above.
(5)
5. Determine the following limit:
lim hx 
x4
 2x2  8
if

 3
where h x   
2 x
if


x4
x4
(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 hx 
x0
(1)
(2)
(3)
(4)
7.
0
8
2
None of the above.
(5)
Determine the following limit:
lim h x 
x 0
(1)
(2)
(3)
(4)
8.
0
8
2
None of the above.
(5)
Determine the following limit:
lim hx 
x0
(1)
(2)
(3)
(4)
9.
0
8
Does not exist.
None of the above.
(5)
Determine the following limit:
lim hx 
x2
(1)
(2)
(3)
(4)
20
2
8
6
None of the above.
(5)
MAT1512/001
10. Determine the following limit:
lim hx 
x2
(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 .
(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

13.
(1) 1
(2)  3
(3) Undefined.
(4) None of the above.
(5)
(4) None of the above.
(5)
lim g  x 
x  2
(1)  2
(2) 1
(3) Undefined.
(4) None of the above.
(5)
14. lim g  x 
x 2
(1)
-2
(2)
-3
(3)
-1
(4)
None of the above.
(5)
15. lim g x 
x 2
(1)  1
(2)  2
(3)  3
(4)
(5)
22
None
of
the
above.
MAT1512/001/01/2022
16.
lim g  x 
x 2

(1)  2
(2)  3
(3) 1
(4) None of the above.
(5)
17.
lim g x 
x 2

(1) 1
(2)  2
(3)  3
(4) None of the above.
(5)
18. Identify the discontinuities in the function g x  graphed above.
(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
(1) 0
(2)
4
2
(3)
2
2
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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
x2
if
x2
if
x2
Determine the values of a and b that make the function f x  continuous at x  2 .