FinalReview.pdf - MATH-UA 122 Calculus II Spring 2017 Practice Final Exam(All Chapters No calculators notes or other outside materials are permitted The

FinalReview.pdf - MATH-UA 122 Calculus II Spring 2017...

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MATH-UA 122 : Calculus II - Spring 2017 Practice Final Exam (All Chapters) No calculators, notes, or other outside materials are permitted. The first two reference pages from the textbook and the formulae for the error bounds will be provided. Show all work to receive full credit. Note: These problems are meant to supplement the examples done in class and for homework, and the review sheet for midterms 1 and 2 . 1. A parametric curve tracing out the circle once clockwise for 0tπstarting at(1, 0)is (a)(cost, sint)(b)(cost,-sint)(c)(cos(2t), sin(2t))(d)(cos(2t),-sin(2t))(e) None of the above. 2. An equation of the tangent to the curvex=t-t-1,y=4+t2at the point corresponding to theparametert=-1 is 3. The graph ofrcosθ+r2=0 is (d) a parabola(e) None of the above. 4. Given the curvesr=3 sinθandr=1+sinθ.(a) Determine both polar and cartesian coordinates for all points of intersection.(b) Find the area of the region insider=3 sinθand outsider=1+sinθ.5. Convert each polar equation into an equation in Cartesian coordinates and then describe the graph:(a)r+cosθ=(b) 4 sinθ=cosθ.6. Find the points at which the polar curver=1+sinθhas horizontal and vertical tangent lines. 7. Given the limaçonr=1+2 cosθ.a. Sketch the graph and give the coordinates of the points at which the curves crosses the coordinateaxes.b. Find the area of the region inside the inner loop.

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