Let F(t)= (-5t² +2,-5e-3, 3 sin(2t)) = 0. Round to 4 decimal places. Find the unit tangent vector T(t) at the point t T(0) =

Q: Compute the derivative of the vector-valued function r(t)=⟨sin2t,et2⟩.

A: In order to compute the derivative of the vector-valued function: Differentiate the vector function…

Q: Find the directional derivative of the function f(, y) = In(x + y°) at the point (- 1,3) in th…

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Q: Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

A: If  is vector valued function which is differentiable and then the unit tangent of is given by

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Q: b) Find Unit vector tangent and normal to the y=x² at P(²₂4) curne

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Q: '] Find the derivative of the function. a) y=c sint+\t cos t b) y = secx+e

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

Q: Let r(t) be a vector-valued function such that the magnitude of r(t) does not change over time. Use…

A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

Q: Consider the vector-valued function r(t)= for t in the interval [0, π]. Find the magnitude of its…

A: Given:The given vector valued function is, Objective:The aim is to determine the magnitude of the…

Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

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Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

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Q: Find Components of the Acceleration For the curve defined by T(t) = (e-t cos(t), e' sin(t)) |3D find…

A: To find- For the curve defined by r→t = e-tcost, et sint, find the unit tangent vector, unit normal…