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Section 1: K/U Multiple Choice: [5 Marks] 1. The lim x->4-7 a) 4 - 2. The lim x-4+ √x² – 16 a) 0 b)-7 c) 0 d) Does Not Exist b) 4 c) 16 d) Does Not Exist 3. The limx-0- x x-7 a) 0 b) infinity c) -7 d) Does Not Exist 4. The lim x-5 x-6 2x-5 a) 5 b) -1 c) -5 d) Does Not Exist 5. For what values of x will the function, f(x) = a) -6,0 b) -6, -3,0 x-3 x3+3x²-18x c) -6,0,3 be discontinuous? d) -3, 0, 6 True or False: [4 Marks] 6. If the limit exists at x = a then the function is continuous at x = a. 7. A removable discontinuity is the only discontinuity in which the limit exists. 8. A cusp is not a discontinuity but does result in the derivative not existing. 9. The reason we use the limit as h→0 to find the slope is because A x →0 Section 2: Communication Limits on a Graph: [5 Marks] 10. Use the graph of f(x) given to determine the following: a) The limX--2- b) The limx+-2+ c) The lim x--2 d) Find f (-2) e) The lim x-→3- -5 W f) The lim x-3+ g) The lim x-3 h) Find x when f(x) = -1 i) The lim x-7 j) Type of discontinuity is at x=-2? 11. Explain what Average Rate of Change and Instantaneous Rate of Change are. Use graphical diagrams and make up an example for each case. [3 Marks]

Section 1: K/U Multiple Choice: [5 Marks] 1. The lim x->4-7 a) 4 - 2. The lim x-4+ √x² – 16 a) 0 b)-7 c) 0 d) Does Not Exist b) 4 c) 16 d) Does Not Exist 3. The limx-0- x x-7 a) 0 b) infinity c) -7 d) Does Not Exist 4. The lim x-5 x-6 2x-5 a) 5 b) -1 c) -5 d) Does Not Exist 5. For what values of x will the function, f(x) = a) -6,0 b) -6, -3,0 x-3 x3+3x²-18x c) -6,0,3 be discontinuous? d) -3, 0, 6 True or False: [4 Marks] 6. If the limit exists at x = a then the function is continuous at x = a. 7. A removable discontinuity is the only discontinuity in which the limit exists. 8. A cusp is not a discontinuity but does result in the derivative not existing. 9. The reason we use the limit as h→0 to find the slope is because A x →0 Section 2: Communication Limits on a Graph: [5 Marks] 10. Use the graph of f(x) given to determine the following: a) The limX--2- b) The limx+-2+ c) The lim x--2 d) Find f (-2) e) The lim x-→3- -5 W f) The lim x-3+ g) The lim x-3 h) Find x when f(x) = -1 i) The lim x-7 j) Type of discontinuity is at x=-2? 11. Explain what Average Rate of Change and Instantaneous Rate of Change are. Use graphical diagrams and make up an example for each case. [3 Marks]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Section 1: K/U Multiple Choice: [5 Marks] 1. The lim x->4-7 a) 4 - 2. The lim x-4+ √x² – 16 a) 0 b)-7 c) 0 d) Does Not Exist b) 4 c) 16 d) Does Not Exist 3. The limx-0- x x-7 a) 0 b) infinity c) -7 d) Does Not Exist 4. The lim x-5 x-6 2x-5 a) 5 b) -1 c) -5 d) Does Not Exist 5. For what values of x will the function, f(x) = a) -6,0 b) -6, -3,0 x-3 x3+3x²-18x c) -6,0,3 be discontinuous? d) -3, 0, 6 True or False: [4 Marks] 6. If the limit exists at x = a then the function is continuous at x = a. 7. A removable discontinuity is the only discontinuity in which the limit exists. 8. A cusp is not a discontinuity but does result in the derivative not existing. 9. The reason we use the limit as h→0 to find the slope is because A x →0
Transcribed Image Text:Section 1: K/U Multiple Choice: [5 Marks] 1. The lim x->4-7 a) 4 - 2. The lim x-4+ √x² – 16 a) 0 b)-7 c) 0 d) Does Not Exist b) 4 c) 16 d) Does Not Exist 3. The limx-0- x x-7 a) 0 b) infinity c) -7 d) Does Not Exist 4. The lim x-5 x-6 2x-5 a) 5 b) -1 c) -5 d) Does Not Exist 5. For what values of x will the function, f(x) = a) -6,0 b) -6, -3,0 x-3 x3+3x²-18x c) -6,0,3 be discontinuous? d) -3, 0, 6 True or False: [4 Marks] 6. If the limit exists at x = a then the function is continuous at x = a. 7. A removable discontinuity is the only discontinuity in which the limit exists. 8. A cusp is not a discontinuity but does result in the derivative not existing. 9. The reason we use the limit as h→0 to find the slope is because A x →0
Section 2: Communication Limits on a Graph: [5 Marks] 10. Use the graph of f(x) given to determine the following: a) The limX--2- b) The limx+-2+ c) The lim x--2 d) Find f (-2) e) The lim x-→3- -5 W f) The lim x-3+ g) The lim x-3 h) Find x when f(x) = -1 i) The lim x-7 j) Type of discontinuity is at x=-2? 11. Explain what Average Rate of Change and Instantaneous Rate of Change are. Use graphical diagrams and make up an example for each case. [3 Marks]
Transcribed Image Text:Section 2: Communication Limits on a Graph: [5 Marks] 10. Use the graph of f(x) given to determine the following: a) The limX--2- b) The limx+-2+ c) The lim x--2 d) Find f (-2) e) The lim x-→3- -5 W f) The lim x-3+ g) The lim x-3 h) Find x when f(x) = -1 i) The lim x-7 j) Type of discontinuity is at x=-2? 11. Explain what Average Rate of Change and Instantaneous Rate of Change are. Use graphical diagrams and make up an example for each case. [3 Marks]
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