| 1. |
Compute the following definite integrals.
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| 2. |
Suppose  . Then what is  ?
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| 3. |
Suppose  . What is  ?
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| 4. |
Suppose  . What is  ?
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| 5. |
Suppose  and  . Then what is  ?
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| 6. |
Find the following areas.
| (a) |
The area under  and above  between  and  .
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| (b) |
The area bounded by  .
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| (c) |
The area bounded by the curves  and  .
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| 7. |
Find the distance between the points with coordinates  and  .
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| 8. |
What is the formula of the sphere centered at (1,2,3) and of radius equal to 5?
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| 9. |
What is the graph of the equation  ?
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| 10. |
Let  . Compute  .
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| 11. |
Find the domain of  .
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| 12. |
Find the domain of  .
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| 13. |
Find the domain of  .
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| 14. |
Compute  for the following functions:
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| 15. |
Classify the following equations as to their order, linearity/non-linearity, and as to whether they have constant coefficients. In all the problems below assume that  is a function of independent variable  .
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| 16. |
Solve the following differential equations:
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| 17. |
Determine whether  satisfies the differential equation  .
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| 18. |
Determine whether  satisfies the differential equation  .
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