| 1. |
Assume the graph below
is the graph of a function  . Sketch the graph of
| (a) |
 (5 points)
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| (b) |
 (5 points)
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| (c) |
 (5 points)
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| 2. |
What are the domains of the following functions:
| (a) |
 (5 points)
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| (b) |
 (5 points)
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| (c) |
 (7 points)
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| 3. |
Let  . What is the domain and a formula for the function
| (a) |
 ? (2 points)
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| (b) |
 ? (2 points)
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| (c) |
 ? (2 points)
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| (d) |
 ? (3 points)
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| (e) |
 ? (3 points)
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| 4. |
Let  be functions defined in some interval containing  . Suppose  , and  . Determine the following limits.
| (a) |
 (2 points)
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| (b) |
 (2 points)
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| (c) |
 (2 points)
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| (d) |
 (3 points)
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| (e) |
 (2 points)
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| (f) |
 (2 points)
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| 5. |
Suppose  is continuous at  and  . What is  ? (2 points)
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| 6. |
Determine if the following limits exist. In cases where the limit does not exist determine whether the left or the right limit exists.
| (a) |
 (2 points)
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| (b) |
 (3 points)
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| (c) |
 (4 points)
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| 7. |
Consider the following graph:
Can this graph be the graph of
| (a) |
 for some positive real number  ? If the answer is “no”, explain why. (5 points)
|
| (b) |
 for some positive real number  ? If the answer is “no”, explain why. (5 points)
|
| (c) |
 for some positive real number  ? If the answer is “no”, explain why. (5 points)
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| (d) |
 for some positive real number  ? If the answer is “no”, explain why. (5 points)
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| 8. |
Compute the following limits.
| (a) |
 (2 points)
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| (b) |
 (3 points)
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| (c) |
 (2 points)
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| (d) |
 (3 points)
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| (e) |
 (5 points)
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| 9. |
Explain how to use the “Squeeze” Theorem to prove that  . (5 points)
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| 10. |
Determine at which points (if any) the following functions are discontinuous. Explain your answer.
| (a) |
 (2 points)
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| (b) |
 (2 points)
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| (c) |
 (5 points)
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| (d) |
 (5 points)
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