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Consider the curve given by the parametric equations

[math]
a.) Determine the point on the curve where the tangent is horizontal.
[math]

b.) Determine the points [math], [math] where the tangent is vertical and [math] .

[math]
[math]

 Use the parametric equations of an ellipse [math] to find the area that it encloses.

Area = 

 

Consider the parametric curve given by the equations [math] [math] How many units of distance are covered by the point [math] between [math] and [math] ?

Answer: 

Which of the following integrals represents the length of the parametric curve [math] about the [math]-axis?







 

Find the length of the curve [math]

Length =

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