Let with . Evaluate…

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Let r(u)=⟨cos⁡u, sin⁡u, ln⁡u⟩r(u)=\langle\cos u,\,\sin u,\,\ln u\rangle with u=t2+1u=t^{2}+1. Evaluate r′(2)r'(2). (a) ⟨−sin⁡5, cos⁡5, 15⟩\langle-\sin 5,\,\cos 5,\,\dfrac{1}{5}\rangle (b) ⟨4sin⁡5, 4cos⁡5, 45⟩\langle4\sin 5,\,4\cos 5,\,\dfrac{4}{5}\rangle (c) ⟨−4sin⁡5, 4cos⁡5, 45⟩\langle-4\sin 5,\,4\cos 5,\,\dfrac{4}{5}\rangle (d) ⟨−2sin⁡5, 2cos⁡5, 25⟩\langle-2\sin 5,\,2\cos 5,\,\dfrac{2}{5}\rangle

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