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Chapter102008 - Chapter 10 Test April 8 2008 No Calculators...

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Chapter 10 Test April 8, 2008 No Calculators Name 1. Find the equation of the normal line to the curve if x = sin 2 t, y = cos2 t where t = 7 p ÄÄÄÄÄÄÄÄ 6 2. If x = e - t and y = e 2 t , then find d 2 y ÄÄÄÄÄÄÄÄÄÄÄÄ dx 2 in terms of t, and discuss the concavity of this plane curve for - • < t < • 3. Find the length of the curve if x = ln H cost L , y = t , and 0 £ t £ p ÄÄÄÄ 3
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4. Solve the initial value problem dr ÄÄÄÄÄÄÄ dt = H cot 2 t L i + i k j j j j j 1 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄ 2 t è!!!!!!!!!!!!!! t 2 - 1 y { z z z z z j where r H 1 L = < 0, 1 > 5. Find the unit vectors H four in all L that are tangent and normal to x = 7 t - t 3 , y = 1 + t 2 - 5 t, at t = 1 6. Find the slope of the tangent line for r = 1 - sin q , at q = p ÄÄÄÄ 2 .
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7. Sketch the graph of the polar equation, and be sure to label at least three polar points H r, q L
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