Consider the vector field v(x) i-j+ 6k. a) Calculate fvo dr, where I is the straight line from (4,0,4) to (0,4,8). b) Calculate fu• dr where C'is the curve from (4,0,4) to (0,4, 8) in the first quadrant given by x? + 4y? = 22 , x +z = 8.

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Q: Define two vector functions F(t) = 8 sin(t)i + 6 cos(t)j + (t – 2)k ü(t) = 6 sin(t)i + 8cos(t)j + (t…

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Q: C

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A: Given :- F →t =  cos πt , e2t-1 , t2 - 1  , G →1 =  1 , 1 , -1G' →1 =  2, 3, 2G'' →1 =  0 , 1 , 0…

Q: Find r'(t), r(t), and r'(to) for the given value of to- r(t) = (e², e²t), to = 0 r'(t) = r(to) =…

A: rt=et,e2t,t0=0

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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