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Find the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.
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- The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe point (x, y) where the slope of the tangent line is largest.The parametric curve defined by [x = 4t - π · sin(2t) ly = 4 - π· cos(2t) is shown. The curve intersects itself at the point (0,4).Compute the derivative dydx of the polar curve r=sin2θ at θ=π3.
- The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe point (x, y) where the slope of the tangent line is smallestFind the solution of polar coordinate f(z) = Z+ sine function by using Cauchy-Riemann method.Find the derivative dydx of the polar function r=sec(2θ) at θ=π4
- The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a limaçon. Findthe points (x, y) and the slopes of the tangent lines at these pointsfor θ = 0.please find the normal plane equation and parametric equations for the tangent line to the curve with the given parametric equations at the specified pointGraph the curve with parametric equations x = sin(t), y = 3 sin(2t), z = sin(3t). Find the total length of this curve correct to four decimal places.