Mathematics

Mathematics

Problem

At θ=0\theta=0, the polar curve defined by r=θ2sin⁡θr=\theta^{2}\sin\theta intersects the origin. Which description best characterizes the tangent line to the curve at that point? a) The tangent is vertical only. b) No horizontal or vertical tangent exists; the slope is a finite non-zero value. c) The tangent is horizontal only. d) Both horizontal and vertical tangents occur at the origin (a cusp).

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