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