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Solved in 4 steps with 3 images
- Find the exact length of the polar curve r=e2(theta) , where 0 is less than or equal too theta is less than or equal too ln(3).Consider the polar curves C1 : r = −3 sin(2θ) and C2 : r = 3 sin θ. 1. What is the equation of the tangent line to C1 at point (√3/2, √3/2)Sketch r = 4 + 8 cos θ on the image below and find the area outside the inner loop of the curve using polar coordinates integration.
- Find the area of the region enclosed by one loop of the curve for the polar equation r = 2sin3θ.Consider the parametric equations x = a cos3 t and y = a sin3 t with 0 ≤ t ≤ π. Find the surface area of the solid obtained by rotating the region about the x-axis.Find the arc length of the polar curve described by: r = 8 + 8cos(theta)
- Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.r = cos(θ/2)θ = πFind the length of the polar curve r = −4 sin θ, 0 ≤θ ≤π. Assume that the curve traces out exactly once for the given range of θ.Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ
- Find the equation of the tangent line to the polar curve r = 3 + 8 sin θ at θ = π/6.Note that sin(π/6) = 1/2, cos(π/6) = √3/2.Use the integration capabilities of a graphing utility to approximate the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 4 cos 2θ, [0, π/ 4]Given two polar curves and r=2cos2θ , r =1 as in Figure 1. Find the area of the shaded region by using the single integration in polar coordinates.