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Unformatted text preview: 2nd Midterm, Calculus 2 Sec 6 04/07/2011 You can solve as many exercises as you want from each one of the sets. Exercises for 10 points are elementary and require short calculations, exer- cises for 15/20 points are intermidiate and exercises for 25/30 points are quite challenging. All the exercises but the first one, are about studying the mag- nitude of certain objects (integrals, sequences, series) and they do not require long calculations. 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. Set 0: The function r ( ) = 1+2 cos ( ) defines a curve in polar coordinates. (15 points) Find vertical and horizontal tangent lines to the curve and not smooth points (if any). (10 points) Find the self intersections of the curve. Set A : Study the convergence of the following improper integrals: 1) Z + 1 arctan x x dx (10 points)...
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