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Honors AP Calculus / Mr. Hansen |
Name: _______________________________ |
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12/13/2012 |
Test #3 (100 points): Chapter 7
General Instructions:
§ No calculator is permitted on today’s test.
§ Simplification is required only where stated.
§ Final answers must be circled in order to earn full credit. Units are required when appropriate.
§ Keep your eyes on your own paper. Exceptions may result in immediate loss of your paper.
§ Show your work. Work is required for credit in each problem.
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Part I. Definitions Define each term. Each
definition must begin with the appropriate part of speech (noun, adjective,
etc.). Circular definitions will earn no credit. |
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1. |
particular solution of a
diff. eq. |
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2. |
separable (in connection
with diff. eqs.) |
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3. |
chaos |
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4. |
second-order differential
equation |
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5. |
slope field |
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Part II. Free Response |
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6. |
Sketch the slope field
(using the lattice points on [–3, 3] |
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7. |
On the slope field you
sketched in #6, sketch the solution having initial condition (1, 2.5). |
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8. |
Is the diff. eq. in #6
separable? (Yes or no.) __________ |
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9. |
Find 3 different initial
conditions for #6, all using exactly the same value of t, and having y values
that vary by less than 0.000001=10–6, such that the 3 initial
conditions give rise to 3 completely different behaviors. Simply state your
ordered pairs. |
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10. |
Prove, rigorously, that
there exists a unique solution to the diff. eq. in #6 that is a straight
line. (Hint: Any line, wlog, must have the property that the rate of change of
its slope equals 0.) |
