Find the Linearization of the Function at the Given Point $f ( x , y , z ) = \tan ^ { - 1 } x y z$

question 13

Multiple Choice

Find the linearization of the function at the given point.
- $f ( x , y , z ) = \tan ^ { - 1 } x y z$ at $( 9,9,9 )$

• A) \(L ( x , y , z ) = \frac { 81 } { 6562 } x + \frac { 81 } { 6562 } y + \frac { 81 } { 6562 } z + \tan ^ { - 1 } 81 - \frac { 243 } { 6562 }\)
• B) \(L ( x , y , z ) = \frac { 81 } { 6562 } x + \frac { 81 } { 6562 } y + \frac { 81 } { 6562 } z + \tan ^ { - 1 } 729 - \frac { 243 } { 6562 }\)
• C) \(L ( x , y , z ) = \frac { 81 } { 531,442 } x + \frac { 81 } { 531,442 } y + \frac { 81 } { 531,442 } z + \tan ^ { - 1 } 729 - \frac { 2187 } { 531,442 }\)
• D) \(\mathrm { L } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \frac { 81 } { 531,442 } \mathrm { x } + \frac { 81 } { 531,442 } \mathrm { y } + \frac { 81 } { 531,442 } \mathrm { z } + \tan ^ { - 1 } 81 - \frac { 2187 } { 531,442 }\)

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Definitions:

Hedge Accounting

An accounting method that recognizes the offsetting position of a hedge in the financial statements to reduce the volatility of earnings.

Foreign Currency Transactions

Deals or business activities that involve the exchange of currencies from different countries, impacting financial statements due to exchange rate changes.

Fair-Value Hedge

A hedge of the exposure to changes in fair value of an asset or liability or an unrecognized firm commitment, which could affect profit or loss.

Forward Contract

a financial agreement between two parties to buy or sell an asset at a future date for a price agreed upon today, commonly used for hedging and speculation.