Find the Coordinates of the Point Where the Line Tangent $\vec { r } ( t ) = t \vec { i } + t ^ { 2 } \vec { j } + t ^ { 3 } \vec { k }$

question 22

Essay

Find the coordinates of the point where the line tangent to the curve $\vec { r } ( t ) = t \vec { i } + t ^ { 2 } \vec { j } + t ^ { 3 } \vec { k }$ at the point (4, 16, 64)crosses the xy-plane.

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Definitions:

Interval of Values

A range of values within which a specified parameter falls, often used in statistics to describe confidence intervals.

Multivariate Data

Data involving two or more variables that are analyzed together to understand patterns and relationships.

Univariate Data

Data consisting of observations on only a single characteristic or variable.

Average Weight

The mean weight calculated by summing all the individual weights and dividing by the number of weights.