Answer True or False, Giving a Reason for Your Answer $\phi ( x , y ) = \ln ( | x y | )$

question 54

Essay

Answer true or false, giving a reason for your answer.Let $\phi ( x , y ) = \ln ( | x y | )$ so that $\nabla \phi = \frac { 1 } { x } \vec { i } + \frac { 1 } { y } \vec { j }$ .
Then $\int _ { C } \nabla \phi \cdot d \vec { r } = \phi ( 1,1 ) - \phi ( - 1,1 )$ where C is given by the parametrization $x = t , y = 1$ for $- 1 \leq t \leq 1$ .

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Definitions:

Market Growth

An increase in the demand for a particular product or service over time, often measured by changes in sales and market share.

Stealing Share

A competitive strategy aimed at gaining market share from competitors by attracting their customers, rather than expanding the overall market.

Forward Selling

The practice of selling goods that are not immediately available but will be in the future.

Forward Buying

Purchasing large quantities of goods when prices are lower to use or sell over time, often to hedge against price increases.