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:

Mann Act

a 1910 U.S. federal law, officially known as the White-Slave Traffic Act, originally intended to combat forced prostitution and human trafficking.

Prostitution

The practice or occupation of engaging in sexual activity with someone for payment.

Human Behavior

The range of actions and mannerisms exhibited by humans, influenced by culture, attitudes, emotions, values, ethics, authority, rapport, hypnosis, persuasion, coercion, and genetics.

White Slave Traffic Act

Also known as the Mann Act, a United States federal law passed in 1910 aimed at preventing the transport of women across state lines for "immoral" purposes.