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) \(1 - 2 x - 6 y + 3 x ^ { 2 } + 24 x y + 27 y ^ { 2 } - 4 x ^ { 3 } - 36 x ^ { 2 } y - 108 x y ^ { 2 } - 108 y ^ { 3 }\)

Know how to manage email folders for efficient message organization.

Understand and identify the components and purpose of hyperlinks.

Recognize the pathway and servers involved in sending email messages.

Describe the functionalities and usage of an email client.

---

Definitions:

Negative-Feedback

A process in which increases in output lead to future decreases in the same output, stabilizing systems against fluctuations.

Aldosterone

A substance generated by the adrenal glands that plays a role in regulating blood pressure through managing the balance of sodium and water in the body.

Hypogastric Region

The lower central part of the abdomen located below the umbilical region.

Umbilicus

Also known as the navel or belly button, it is the scar on the abdomen that marks the former attachment point of the umbilical cord.