Use Taylor's Formula to Find the Requested Approximation of F(x $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \mathrm { e } ^ { \mathrm { x } + 3 \mathrm { y } }$

question 238

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Quadratic approximation to $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \mathrm { e } ^ { \mathrm { x } + 3 \mathrm { y } }$

• A) \(x + 3 y + \frac { 1 } { 2 } x ^ { 2 } + \frac { 3 } { 2 } x y + \frac { 9 } { 2 } y ^ { 2 }\)
• B) \(1 + x + 3 y + \frac { 1 } { 2 } x ^ { 2 } + 3 x y + \frac { 9 } { 2 } y ^ { 2 }\)
• C) \(x + 3 y + \frac { 1 } { 2 } x ^ { 2 } + \frac { 9 } { 2 } y ^ { 2 }\)
• D) \(1 + x + 3 y + \frac { 1 } { 2 } x ^ { 2 } + \frac { 9 } { 2 } y ^ { 2 }\)

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