(1) Consider the parametrized curve /2+), 7(t) = ( 13 (1 + 1)/, 1/3(1 1)/2,...

 

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(1) Consider the parametrized curve √/2+), 7(t) = ( 13 (1 + 1)³/², 1/3(1 − 1)³/²2, - -1 < t < 1. (a) Show that y is a unit speed curve. (b) Find (simplified) expressions for the vector fields along that constitute the Frenet frame. That is, find the unit tangent T(t), the unit normal N(t), and the binormal B(t). (c) Find (simplified) expressions for the curvature (t) and the torsion r(t) of the curve y. (d) Consolidate the previous results into the Frenet equations for the unit speed curve y. (1) Consider the parametrized curve √/2+), 7(t) = ( 13 (1 + 1)³/², 1/3(1 − 1)³/²2, - -1 < t < 1. (a) Show that y is a unit speed curve. (b) Find (simplified) expressions for the vector fields along that constitute the Frenet frame. That is, find the unit tangent T(t), the unit normal N(t), and the binormal B(t). (c) Find (simplified) expressions for the curvature (t) and the torsion r(t) of the curve y. (d) Consolidate the previous results into the Frenet equations for the unit speed curve y.

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a To show that is a unit speed curve we need to demonstrate that the magnitude of its derivative wit... View the full answer