- $$r ( t ) = ( 10 \sin t ) i - ( 3 \cos 3 t ) j + e ^ { - 8 t _ { k } } \mathbf { k } ; t _ { 0 } = 0$$

question 13

Multiple Choice

$\text { For the smooth curve } r ( t ) \text {, find the parametric equations for the line that is tangent to } r \text { at the given parameter value } t = t _ { 0 } \text {. }$
- $$r ( t ) = ( 10 \sin t ) i - ( 3 \cos 3 t ) j + e ^ { - 8 t _ { k } } \mathbf { k } ; t _ { 0 } = 0$$

• A) x = 10, y = -3t, z = -8 + t
• B) x = 10t, y = -3, z = 1 - t
• C) x = 10t, y = 3, z = 1 + t
• D) x = 10t, y = -3, z = 1 - 8t

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Essential Feature

A core characteristic or component that is necessary for the function or identity of something.

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