Given $f ( x , y ) = x e ^ { - 2 y }$

question 281

Essay

Given $f ( x , y ) = x e ^ { - 2 y }$ , at the point $( 4,0 )$ find the equation of the tangent plane to the graph of $f$ . Also, find a normal vector to the graph of $f$ .

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Definitions:

Content Analysis

A research technique used to objectively and systematically analyze the content of communication material.

Qualitative Data Sets

Qualitative data sets comprise non-numeric data used in research to describe attributes, properties, and characteristics, often gathered through interviews, observations, and textual analysis.

Themes

Central topics, subjects, or ideas that are recurrently explored in various forms of art, literature, music, or discussion, providing a deeper understanding or interpretation of the content.

Sampling Weights

Statistical adjustments applied to samples to account for unequal probabilities of selection due to the sampling design, ensuring representativeness.