Use Taylor's Formula to Find the Requested Approximation of F(x $10 x + y + 5 x ^ { 2 } + \frac { 1 } { 2 } y ^ { 2 }$

question 290

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Quadratic approximation to f(x, y) = sin(10x + y)

• A) \(10 x + y + 5 x ^ { 2 } + \frac { 1 } { 2 } y ^ { 2 }\)
• B) \(10 x + y + 5 x ^ { 2 } + \frac { 1 } { 2 } x y + \frac { 1 } { 2 } y ^ { 2 }\)
• C) \(10 x + y\)
• D) \(10 x + y + 5 x ^ { 2 } + y ^ { 2 }\)

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