Find the unit tangent vector to the curve given below at the specified point. r(t) = 7ti−2t²j¸ t = 4 O T(4) = O T(4)= O T(4)= T(4)= 7 305 -2 305 7 305 i- -i- i- 16 √305 i- 16 305 2 305 14 16 √305 √305 j

Q: Let F(t) = (-t² + 3, e-3t, - 2 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 -

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Q: YouTrylt 1 Find the derivative of the vector function. r(t) =(t sint, t, 1 cos(2t ) C.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: Sketch the curve. Show the tangent vector at t = 0. Mark the initial and final points, and any other…

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Q: x²+4 Compute the derivative of the vector-valued function: r(t) = ln- x-5 i+ sin ² tj + (t² + 1)²k

A: Given vector valued function r(t)=lnx2+4x-5i+sin2tj+t2+12k The objective is to compute the…