Find the Quadratic Approximation to the Function F(x, Y)= Cos $f ( x , y ) = 1 - \frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 2 }$

question 103

Multiple Choice

Find the quadratic approximation to the function f(x, y) = cos x cos y valid near the origin.

• A) \(f ( x , y ) = 1 - \frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 2 }\)
• B) \(f ( x , y ) = 1 + \frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 2 }\)
• C) \(f ( x , y ) = 1 - \frac { x ^ { 2 } } { 2 } - \frac { y ^ { 2 } } { 2 }\)
• D) \(f ( x , y ) = 1 - x ^ { 2 } - y ^ { 2 }\)
• E) \(f ( x , y ) = 1 - \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 4 }\)

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Definitions:

Embryonic Period

The stage of prenatal development from fertilization up to the eighth week, where rapid growth and development of major body systems and structures occur.

Spine and Brain

Central components of the nervous system where the brain is the control center and the spine connects it to the rest of the body through nerve fibers.

Germinal Period

The initial two weeks of prenatal development after conception, characterized by rapid cell division and the beginning of cell differentiation.

Fetal Stage

The fetal stage is the last stage of prenatal development, beginning in the ninth week of pregnancy and continuing until birth, characterized by rapid growth and maturation of organs and body systems.