fall17mth143.practice2.9-ParametricCalc.pdf

# X y b use calculus to find the cartesian coordinates

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( x , y ) = ( , ) (b) Use calculus to find the Cartesian coordinates of the left- most point on the parametric curve. ( x , y ) = ( , ) (c) Find the horizontal asymptote for this curve. y = (d) Find the vertical asymptote for this curve. x = Answer(s) submitted: (incorrect) Correct Answers: exp(1) 1/exp(1) -1/exp(1) -1*exp(1) 0 0 8. (1 point) Find the slope of the tangent line to the trochoid x = rt - d sin ( t ) , y = r - d cos ( t ) in terms of t , r , and d . Slope = Answer(s) submitted: (incorrect) Correct Answers: d*sin(t)/(r-d*cos(t)) 9. (1 point) Consider the following parametric equation. x = 11 ( cos θ + θ sin θ ) y = 11 ( sin θ - θ cos θ ) What is the length of the curve for θ = 0 to θ = 5 8 π ? Answer: Answer(s) submitted: (incorrect) Correct Answers: .5*11*(5*pi/8)ˆ2 10. (1 point) Calculate the length of the path over the given interval. ( sin4 t , cos4 t ) , 0 t π Solution: Solution: We have x = sin4 t , y = cos4 t , hence x 0 = 4cos4 t and y 0 = - 4sin4 t . By the formula for the arc length we obtain: S = Z π 0 q x 0 ( t ) 2 + y 0 ( t ) 2 dt = Z π 0 p 16cos 2 4 t + 16sin 2 4 t dt = Z π 0 16 dt = Answer(s) submitted: (incorrect) Correct Answers: 4*pi 2

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11. (1 point) Find the area under one arch of the trochoid x = 8 θ - 4sin ( θ ) , y = 8 - 4cos ( θ ) .
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