(b) Given the vector function F(t) = () i + () - j+ (tan-t) k. %3D Find F(t) dt

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Q: 2. Let T(x; y) = sin(2x – y) , P (-; ) and Q(0;0) (a) Determine the directional derivative of T at P…

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Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

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Q: x-1 y-2 z-1 2 -6 7 1 F(t) = ( 21 + ¹ )i + ¹/ (m² − 3)} j + t√21³-1k at t=1 1 4 (c) show that the…

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Q: Find the derivative of the vector function r(t) = In(13 – t²)i+ y13+tj– 9e 3 k r'(t) = {

A: The given vector function is                                   r(t)=ln13-t2i+13+tj-9e-3tk

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Q: Find the second derivative of the vector-valued function F(t) (4t + 3 sin(t))i + (6t + 4 cos(t))…

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Q: Find the derivative of the vector function r(t) = In(13 – ) i+ v3 +ij+ le- k r' (t) = (

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Q: Find the second derivative of the vector-valued function F(t) = (5t + 4 sin(t))² + (2t + 4 cos(t))…

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Q: b. Find the directional derivative of the function f(r, y, z) = re" + ye + ze" at the point (1, 1,…

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Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2.1,7",e-7) from 0 to…

A: The detailed solution of the problem is given in the next steps.

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Q: Find the derivative of the vector function r(t)=ln⁡(7−t^2)i+sqrt(8+t)j−5e^(2t)k r′(t)=⟨  ,  ,  ⟩

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Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= a(7- sin 0) and =7, where a…

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Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t

A: The velocity and acceleration in terms of ur→ and uθ→ are given by: v→=r'ur→+r θ'uθ→a→=r''-r…

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A: By using derivative of function

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