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# mid2n - x = cos t y = sin t-cos t 2 Consider the curve...

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Math 126 C - Winter 2006 Mid-Term Exam Number Two February 16, 2006 Name: Section: 1 10 2 10 3 10 4 10 5 10 6 10 Total 60 Complete all questions. You may use a scientifc, non-graphing calculator during this examination. Other elec- tronic devices are not allowed, and should be turned o±± ±or the duration o± the exam. I± you use a trial-and-error or guess-and-check method, or read a numerical solution ±rom a graph on your calculator, when an algebraic method is available, you will not receive ±ull credit. You may use one hand-written 8.5 by 11 inch page o± notes. Show all work ±or ±ull credit. You have 50 minutes to complete the exam. .

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1. Eliminate the parameter in the following parametric equation pair to get a Cartesian equation for the curve that involves no trigonometric functions.

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Unformatted text preview: x = cos t, y = sin t-cos t 2. Consider the curve defned parametrically by the parametric equations x = ln ln t, y = ln t-(ln t ) 2 . Find the equation o± the tangent line to the curve at the point t = e . 3. Find the parametric equations for the tangent line to the curve de±ned by x = t 3-t, y = t 6 + t 2 + 1 , z = 1 2 t 2 + 5 t at the point (0 , 1 , 0) . 4. At what point does the curve y = e x have maximum curvature? 5. Find the length of the curve de±ned by v r ( t ) = a 2 √ 2 3 t 3 / 2 , t, 1 2 t 2 A , ≤ t ≤ 4 6. Find the curvature of the curve de±ned by v r ( t ) = a 1 2 t 2-2 t, t 2-t, t 2 + t A at the point t = 0 ....
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mid2n - x = cos t y = sin t-cos t 2 Consider the curve...

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