m114-se2 - MATH 114 Sample Final Exam 2 1 Consider the line that is tangent to the cycloid given by the parametric equations x = sin y = 1 cos at = At

m114-se2 - MATH 114 Sample Final Exam 2 1 Consider the line...

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MATH 114 – Sample Final Exam 21. Consider the line that is tangent to the cycloid given by the parametric equationsx=θ-sinθ,y= 1-cosθ, atθ=π. At what point (0, y) does this line meet they-axis?(a) (0,1)(b) (0,2-1)(c) (0,0)(d) (0,2)(e) (0,π2-1)(f) (0,2-π2)(g) (0, π)(h) (0, π-2)2. The arc length of the curve given parametrically byx= 3t2,y= 2t3for 0t1is3. What is the area inside one petal ofr= 2 sin(3θ)?4. Consider the graph given parametrically byx= 1 + 2eRt0cos(s+1)dsy=-3-6eRt0cos(s+1)ds.Find the area between the graph and thexaxis, and between the linesx=-2andx= 0.

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