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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