Question 5. Consider the parametric equation x = 27 cos³0 and y = 27 sin³ 0. (a) Find the Cartesian equation of this parametric curve. (b) Find the arc length of this curve in the interval [0, 2π].

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A: The given function gx=lntan x on 0, π. We have to find its domain and range.

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A: We have to find the area enclosed by the curves using integration.

Q: 2- Find the equation of the tangent line to the curve 9xCos(7y) + 5y = 9 at y = 0.

A: To find the equation of the tangent line to the curve 9x cos7y+5y=9 at y=0.

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Q: Question What are the critical points for the plane curve defined by the equations a(t) = sin(nt +),…

A: Let's find critical points.

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Q: Graph these two function, then find the area between them: f(x) = x², g(x) = 4x - x²

A: Topic:- application of derivatives

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Q: 2- Find the equation of the tangent line to the curve 9xCos(7y) + 5y = 9 at y = 0.

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Q: Determine the area of the region bounded by y = Area = || 3x x3 and y=- on the interval [1,10].

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Q: Find the angle , in radians, in the given right triangle. The length of the side adjacent to is 19…

A: To find the value of the angle θ