Use Taylor's Formula to Find the Requested Approximation of F(x $f ( x , y ) = \frac { 1 } { ( 1 + x + 3 y ) ^ { 2 } }$

question 331

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Cubic approximation to $f ( x , y ) = \frac { 1 } { ( 1 + x + 3 y ) ^ { 2 } }$

• A) \(1 + 2 x + 6 y - 3 x ^ { 2 } - 18 x y - 27 y ^ { 2 } + 4 x ^ { 3 } + 36 x ^ { 2 } y + 108 x y ^ { 2 } + 108 y ^ { 3 }\)
• B) \(1 + 2 x + 6 y - 3 x ^ { 2 } - 24 x y - 27 y ^ { 2 } + 4 x ^ { 3 } + 36 x ^ { 2 } y + 108 x y ^ { 2 } + 108 y ^ { 3 }\)
• C) \(1 - 2 x - 6 y + 3 x ^ { 2 } + 18 x y + 27 y ^ { 2 } - 4 x ^ { 3 } - 36 x ^ { 2 } y - 108 x y ^ { 2 } - 108 y ^ { 3 }\)
• D) \(1 - 2 x - 6 y + 3 x ^ { 2 } + 24 x y + 27 y ^ { 2 } - 4 x ^ { 3 } - 36 x ^ { 2 } y - 108 x y ^ { 2 } - 108 y ^ { 3 }\)

---

Definitions:

Sexual Abuse

Any undesired sexual activity by one person upon another, often using coercion or abuse of power.

Preschoolers

Children who are typically between the ages of 3 and 5 years old and attend an early childhood education program before kindergarten.

Fake Memory

A memory that feels real to the person remembering it but is either entirely fabricated or significantly distorted from what actually happened.

Imagine

The ability to form new images and sensations in the mind that are not perceived through senses such as sight, hearing, or other senses.