Find Parametric Equations of the Tangent Line to the Curve $\mathbf { r } ( t ) = \langle t , \sqrt { 2 } \cos t , \sqrt { 2 } \sin t \rangle$

question 50

Essay

Find parametric equations of the tangent line to the curve $\mathbf { r } ( t ) = \langle t , \sqrt { 2 } \cos t , \sqrt { 2 } \sin t \rangle$ at $\left( \frac { \pi } { 4 } , 1,1 \right)$ . Then sketch the curve and its tangent line.

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