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

question 81

Multiple Choice

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

• A) \(1 + x + 2 y + \frac { 1 } { 2 } x ^ { 2 } + 2 x y + 2 y ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } y + \frac { 4 } { 3 } x y ^ { 2 } + \frac { 4 } { 3 } y ^ { 3 }\)
• B) \(1 + x + 2 y + \frac { 1 } { 2 } x ^ { 2 } + 1 x y + 2 y ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + 1 x ^ { 2 } y + 2 x y ^ { 2 } + \frac { 4 } { 3 } y ^ { 3 }\)
• C) \(1 + x + 2 y + \frac { 1 } { 2 } x ^ { 2 } + 1 x y + 2 y ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } y + \frac { 4 } { 3 } x y ^ { 2 } + \frac { 4 } { 3 } y ^ { 3 }\)
• D) \(1 + x + 2 y + \frac { 1 } { 2 } x ^ { 2 } + 2 x y + 2 y ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + 1 x ^ { 2 } y + 2 x y ^ { 2 } + \frac { 4 } { 3 } y ^ { 3 }\)

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Definitions:

T Cells

A type of white blood cell that plays a central role in the immune response, assisting in the protection against pathogens.

Macrophages

A variant of white blood cell that consumes and dismantles cellular rubbish, alien substances, microorganisms, and cancer cells via a mechanism termed phagocytosis.

Red Blood Cells

The cells in the blood which carry oxygen from the lungs to the body's tissues and carbon dioxide back to the lungs.

Macrophages

Immune cells that engulf and digest cellular debris, foreign substances, microbes, and cancer cells in a process called phagocytosis.