Q3) For the vector function f(t) = [2e", te?, 3 te? 1, Determine the point of %3D tangency and the unit tangent vector when t = 2. %3D

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A: ### Part (a)Given: V = R^2, u = (2, 6), and W = { (x, y) | y = 4x }.A basis for W can be v = (1, 4).…

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Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

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A: Given, r→t=12t2, t2, lnt Used differentiation formulas, ddxxn=nxn-1ddxlnx=1xddxCfx=Cddxfx    C is…

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Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

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