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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Definitions:

P(A ∩ B)

The probability that events A and B both occur at the same time.

P(A ∪ B)

The probability of the occurrence of at least one of two events, A or B.

P(A ∩ B)

The probability that both events A and B occur at the same time.

Convergent Thinking

A cognitive process in which one focuses on arriving at a single, correct solution to a problem, as opposed to generating multiple solutions.