Use Taylor's Formula to Find the Requested Approximation of F(x $f ( x , y ) = \frac { 1 } { ( 1 + x + 6 y ) ^ { 2 } }$

question 54

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Quadratic approximation to $f ( x , y ) = \frac { 1 } { ( 1 + x + 6 y ) ^ { 2 } }$

• A) \(1 + 2 x + 12 y + 3 x ^ { 2 } + 36 x y + 108 y ^ { 2 }\)
• B) \(1 + 2 x + 12 y + 3 x ^ { 2 } - 36 x y + 108 y ^ { 2 }\)
• C) \(1 - 2 x - 12 y + 3 x ^ { 2 } + 36 x y + 108 y ^ { 2 }\)
• D) \(1 - 2 x - 12 y + 3 x ^ { 2 } - 36 x y + 108 y ^ { 2 }\)

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Definitions:

Indefinite Period

A duration without a specified end date, often used in contracts or agreements to denote an ongoing arrangement.

Periodic Tenancy

The tenancy that exists when the landlordand tenant agree that rent will be paid in regular successive intervals until notice to terminate is given but do not agree on a specific duration of the lease. A typical periodic tenancy is atenancy from month to month.

Month-To-Month Lease

A rental agreement that renews each month automatically until either the tenant or landlord provides notice to terminate.

Duty To Mitigate

The legal obligation to make reasonable efforts to minimize the damage caused by a breach of contract or other wrongful act.