Let and . Determine at…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let r(t)=⟨t2,t,1⟩\mathbf r(t)=\langle t^{2},t,1\rangle and s(t)=⟨sin⁡t,cos⁡t,t⟩\mathbf s(t)=\langle\sin t,\cos t,t\rangle. Determine ddt(r(t)⋅s(t))\displaystyle \frac{d}{dt}\big(\mathbf r(t)\cdot\mathbf s(t)\big) at t=0t=0. (a) 00 (b) 22 (c) 33 (d) 11

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