Given the following vector field and orientated curve C, evaluate F-Tds. (x.y) 3/2 on the curve r(t) = (31?.81), for 1sts2

Q: Draw the slope field (direction field) for the following DE: y'=y-t

A: Given DE is Make table as follows:…

Q: Let F(t) = (1, ²,4) and P = (2, 10, 4). Consider the curve C parametrized by F(t). Compute a tangent…

A: The objective of the question is to find the tangent vector, unit tangent vector, and the tangent…

Q: For the vector-valued function r, carry out the following steps. a. Evaluate lim r(t) and lim r(t),…

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Q: Let 7(t) = (t + 4, – e*, 3 sin(3t)) - Find the unit tangent vector T (t) at the point t = :0 T(0) =

A: We have to find

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Let r(t) = (-3t³-4, -3e¹, 5 sin( - 3t)) Find the unit tangent vector T' (t) at the point t = 0 T(0)…

A: r(t)=<-3t3-4, -3e4t, -5Sin(-3t) >

Q: Answer the following questions involving the vector-valued function 7 (t) cos(at),sin(at)): (a)…

A: Please see the answer below

Q: Let 7 (t) = (4t³ – 4, – 3e", – 3 sin( – 4t)) - Find the unit tangent vector T(t) at the point t = 0…

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Q: Find the unit tangent vector at the indicated point of the vector function 11t 11t 11t costi + e¹¹t…

A: Given rt=e11tcost i^+e11tsint j^+e11t k^

Q: Let 7(t) = (3 cos(t), 3 sin(t), 3t) and P = (3, 0,6). Consider the curve c parametrized by F(t).…

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