Let $f ( x , y , z ) = \sqrt { 2 x + 3 y - z }$

question 93

Essay

Let $f ( x , y , z ) = \sqrt { 2 x + 3 y - z }$ . Find the rate of change of $f$ at the point $( 1,1 , - 4 )$ in the direction $\mathbf { u }$ where $\mathbf { u }$ is a unit vector making an angle $\theta = 60 ^ { \circ }$ with $\nabla f$ .

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Definitions:

Motion To Dismiss

A legal filing requesting the court to rule that the plaintiff's case is insufficient on its face and should be thrown out without further evidence or trial.

Motion For A New Trial

A formal request to a court to nullify a jury's verdict and order a new trial, typically on the basis of procedural errors or issues affecting the fairness of the trial.

Minitrial

A voluntary, private, informal trial with a goal to facilitate dispute resolution between parties, often with an advisor or judge who provides a non-binding verdict.

Summary Judgment

A legal ruling where the court decides a case without a full trial because there's no dispute on the key facts.