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Honors AP Calculus / Mr. Hansen |
Name: _______________________________________ |
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12/7/2006 |
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Test on Chapter 6
Calculator is permitted throughout.
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1. |
State and prove the chain
rule for integrals. |
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2. |
Write 5x as 3 to some
power. |
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3. |
In computer science, it is
often of great value to compute the base-2 logarithm of a number. For
example, log2 32 = 5. |
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(a) |
Develop a procedure for
using your calculator to find the base-2 logarithm of any positive number.
Write instructions for your procedure so that a Third Former could understand
them. |
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(b) |
Verify that your procedure
works correctly for computing log2 63. (Give the answer.) |
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(c) |
Prove that your procedure
works in general, i.e., for all positive numbers. |
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4. |
Compute ∫ x2 sec x3 dx. |
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5. |
Compute |
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6. |
Compute |
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7. |
Compute |
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8. |
Compute |
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9. |
Compute |
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10. |
State L’Hôpital’s
Rule, including the part about what to do if the limit does not exist. |
