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Unformatted text preview: line is horizontal or vertical. b) Verify that the point ( c, 0) is on the curve for any c > 0. How many tangent lines does the curve have at the point ( c, 0)? What are their slopes? Check your answer numerically (for c = 1 4 , c = 1 and c = 4) by drawing the tangent lines on your graphing calculator. c) Consider the curve corresponding to c = 1 3 . Part of this curve is a loop. Find the length of that loop. 4. Find the Cartesian coordinates of all points of intersection of the curves with polar equations r 2 = 4 sin θ and r = 1sin θ . Sketch these curves on the same coordinate axes. Warning (0 , θ 1 ) and (0 , θ 2 ) represent the same point always ; so do ( r, θ ) and (r, θ ± π )....
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 Spring '11
 SOSA
 Calculus, Cartesian Coordinate System, Polar coordinate system, parametric curve

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