Estimate the Error in the Quadratic Approximation of the Given $$f ( x , y ) = \ln ( 1 + 3 x + 4 y ) , \quad | x | \leq 0.1 , | y | \leq 0.1$$

question 401

Multiple Choice

Estimate the error in the quadratic approximation of the given function at the origin over the given region.
- $$f ( x , y ) = \ln ( 1 + 3 x + 4 y ) , \quad | x | \leq 0.1 , | y | \leq 0.1$$

• A) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.1422\)
• B) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.2327\)
• C) \(| E ( x , y ) | \leq 0.012\)
• D) \(| E ( x , y ) | \leq 0.1707\)

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Definitions:

Unrealized Profit

Profits that have been earned but not yet realized through a transaction, often related to investments that have increased in value but have not been sold.

Consolidation Purposes

The process of combining financial statements of separate business entities within a group for reporting as one entity.

Unrelated Party

A party or entity that does not have a familial, business, or financial relationship with another party, ensuring transactions are conducted at arm's length.

Straight-Line Method

A method of calculating depreciation of an asset whereby the cost is evenly distributed over its useful life, resulting in a constant annual depreciation expense.