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Honors AP Calculus / Mr. Hansen |
Name: _______________________________________ |
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10/12/2006 |
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E-mail address (legibly,
please): __________________________ |
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Mr. Hansen’s use only (bonus point for spare
batteries): _______ |
Quest through §4-6
Please read:
Calculator is OK throughout. Each problem
is worth 8 points (with no partial credit), except for the proof, which is
worth 15 points with a possibility of partial credit. Please double-check your
answers carefully.
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1. |
Compute the derivative of y = (sec x)/(cos x) by first rewriting as a power of a single trigonometric function. |
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2. |
Compute the derivative
requested in #1 by a different method. |
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3. |
Find y˘ if y = tan–1 (4x3 – p14). |
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4. |
Find dq/dt
if q(t) = (4t4 – 11t3
+ 2t2 – 11t + 4)(–6t3 – 4t2
+ 13t – 7). |
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5. |
Write instructions for a
younger student, or a student in a different class, to explain how to plot
the graph of y = csc–1 x. |
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6. |
Accepting the product rule
(PR) as a given, prove the quotient rule (QR). |
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7. |
Let f (n) (x) denote the
nth derivative of function f. If f is an odd function with derivatives of all orders, what can you
conclude about |
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(a) |
f (2n) (x), if all we know about f
is what is given above |
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(b) |
f (2n + 1) (x), if it is also known that f
is a polynomial of degree n |
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8. |
Prove (by mathematical
induction) that the sum of the first n
integral multiples of 3 equals 1.5(n2
+ n). |