Find a parametrization of the tangent line at the point indicated. 𝐫(s)=(lns) 𝐢+s^-1 𝐣+9 s 𝐤,

step 1 In this question we have the vector value of function R of S is equal to log of S i cap S to the

Find a parametrization of the tangent line at the point...

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Key Concepts

Vector-Valued Functions

A vector-valued function assigns a vector to each value of a parameter, typically representing a curve or path in space. This concept is essential because it describes how each coordinate of a point changes with the parameter, allowing the analysis of geometric properties and motions along curves.

Derivative of a Vector-Valued Function

The derivative of a vector-valued function with respect to its parameter provides a tangent vector at each point along the curve. This tangent vector indicates the direction and rate of change of the curve, which is fundamental in understanding and finding the equation of the tangent line at a specific point.

Tangent Line to a Curve

The tangent line at a specific point on a curve is the line that best approximates the curve near that point. Its parametrization can be obtained by using the point on the curve and the tangent vector derived from the derivative of the vector-valued function; this process involves evaluating the derivative at the given parameter value and using it to form the linear equation for the tangent line.

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