Suppose C Is the Curve Given by the Vector Function $\mathbf { r } ( t ) = \left\langle t , t ^ { 2 } , 1 - t ^ { 2 } \right\rangle$

question 58

Essay

Suppose C is the curve given by the vector function $\mathbf { r } ( t ) = \left\langle t , t ^ { 2 } , 1 - t ^ { 2 } \right\rangle$ . Find the unit tangent vector, the unit normal vector, and the curvature of C at the point where t = 1.

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