Question

Let r(t) = <t^2, 1 - t, 4t> . Calculate the derivative of r(t) . a(t) at t = 7 assuming that a(7) = <2, -3, 8> a'(7) = <2, 5, 6> (Use decimal notation. Give your answer as a whole or exact number.) d/dt(r(t) . a(t))|_{t=7} =

          Let r(t) = <t^2, 1 - t, 4t> . Calculate the derivative of r(t) . a(t) at t = 7 assuming that
a(7) = <2, -3, 8>
a'(7) = <2, 5, 6>
(Use decimal notation. Give your answer as a whole or exact number.)
d/dt(r(t) . a(t))|_{t=7} =

Added by Kimberly S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

05/25/2024

Step 1

We are given the vector function \( r(t) = (t^2, 1-t, 4) \) and another vector function \( a(t) \) with \( a(7) = (2, -3, 8) \) and \( a'(7) = (2, 5, 6) \). We need to calculate the derivative of the dot product \( r(t) \cdot a(t) \) at \( t = 7 \). Show more…

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Let r(t) = <t^2, 1 - t, 4t> . Calculate the derivative of r(t) . a(t) at t = 7 assuming that a(7) = <2, -3, 8> a'(7) = <2, 5, 6> (Use decimal notation. Give your answer as a whole or exact number.) d/dt(r(t) . a(t))|_{t=7} =