Use the formula T = T(t) = [r'(t) = r²(e)] - '"(t) x Ir'(t) x r"(t)|2 T(0) = r(t) = 7t, to find the torsion of the following curve at a general point. Find torsion at the point corresponding to t = 0.

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A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

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A: A detailed solution is given below.

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A: Curvature K = |r' x r"|/|r'|^3

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A: First we will plot the given parameters.

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A: Suppose r'(t) has units of m/s. To explain why Let r(t) be a differential vector valued functionNow…

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Q: Find the standard form for the TANGENT PLANE to the surface: : = f (x,y) = x cos (xy) at the point…

A: The given function is  z = f(x,y) =x cos(xy)