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Unformatted text preview: Final exam, Calculus 2 Sec 6 05/10/2011 You can solve as many exercises as you want from each one of the sets. You are allowed to use formulas from the list included with the test, but you have to justify every other calculation. Motivate your answers!!! I will give no credit to a correct answer with no motivation, or a correct answer with a wrong motivation. Everything you turn in will be graded and contribute to the final score. The number of points associated to each question reflects the difficulty of that question, but not necessarily the length of the calculation. Set O Parametric curves: 1. (15 points) Calculate the area of the region enclosed by the x-axis and the curve: ( x = 1 + e t y = t- t 2 2. (20 points) Let C be the polar curve r = 1- 2 sin . Find vertical, horizontal tangents and non smooth points. Find self intersections and symmetries. Sketch a graph of the curve. Set A Calculate the following primitives: 1. Z cos x dx 10 points 2. Z e 1 x x 3 dx 10 points 1 3. Z ln(cos x ) cot x dx 10 points 4. Z 1 p 1 + x dx 15 points 5. Z 1 2 + cos x dx 15 points 6. Z e 5 x + e 7 x e x + e- x dx 15 points 7. Z 1 (1- x 2 ) 3 2 dx 15 points Set B Calculate the following limits (the limit might not exist): 1....
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