Polar Coordinates Ï = x 2 + y 2 , θ = arctan (y/n) give where Ï'

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Polar Coordinates ρ = ˆšx2+ y2, θ = arctan (y/n) give

p² + p² d0, 12

where ρ' = dρ/dθ. Derive this. Use it to find the total length of cardioid ρ = α(1 - cos θ). Sketch this curve.

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