 # Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=e^{-8t} cos(8t), y=e^{-8t} sin(8t), z=e^{-8t}, (1, 0, 1) Ernstfalld 2021-02-06 Answered
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
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Step 1 Write the expression to find the parametric equations for a line through the point
Step 2 Write the parametric equations of the curveas follows. Step 3 Write the vector equation from the parametric equations of the curve as follows. Step 4 The tangent vector of the curve is the derivative of the vector function r(t). To find the derivative of the vector function, differentiate each component of the vector function.

Step 5 Given that the point . That is,

As the specified point , consider the value of scalar parameter t as 0 and substitute in the parametric equations of the curve to obtain the point, which is on the required line. Substitute 0 for t in equation (2),

The point on the required line is As the point on the required line is same as the specified point Step 6 Substitute 0 for t in