Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = (tan-¹(t), 2e6t, 12tet), t = 0 T(0) =

Q: Find the unit tangent vector for the parameterized curve: r(t) = 2ti + 2cos tj - 2 sint k

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Q: 21. For the curve 7(t) = sin ti + cos tj, find 7 '(t) and sketch the position vector 7(÷) and the…

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Q: Exercise. The position vector for a particle is described by the vector-valued function: sin(at)…

A: “Hey, since there are two questions posted, we will answer first question. If you want any specific…

Q: 2. Given that r(t) = 2 sin ti + 2 cos tj+ tan tk. Find the unit tangent vector T(t) at the point…

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Q: r(t) = cos(t)i + V2 sin(t)j+ cos(t)k. Find the unit tangent vector T(t), the curvature K(t), the…

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Q: A curve is parametrized by the given equations. Find the equation of the tangent line to the curve…

A: Equation of the tangent line

Q: 1. Consider the position function 7 (t) = (4 sin(2t), 2,4 cos(2t)). (a) Sketch the path of this…

A: Curvature: The curvature of postion function r→(t) is given by, κ(t) = T'(t)r'(t) Given: r→(t) =…

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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