Use Taylor's Formula to Find the Requested Approximation of F(x $6 x + y - 36 x ^ { 3 } - 18 x ^ { 2 } y - 3 x y ^ { 2 } - \frac { 1 } { 6 } y ^ { 3 }$

question 62

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Cubic approximation to f(x, y) = sin(6x + y)

• A) \(6 x + y - 36 x ^ { 3 } - 18 x ^ { 2 } y - 3 x y ^ { 2 } - \frac { 1 } { 6 } y ^ { 3 }\)
• B) \(6 x + y - 36 x ^ { 3 } - \frac { 1 } { 6 } y ^ { 3 }\)
• C) \(6 x + y - 72 x ^ { 3 } - \frac { 1 } { 3 } y ^ { 3 }\)
• D) \(6 x + y - 72 x ^ { 3 } - 18 x ^ { 2 } y - 3 x y ^ { 2 } - \frac { 1 } { 3 } y ^ { 3 }\)

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Definitions:

Mean

The arithmetic average of a set of numbers, calculated by adding them together and dividing by the number of terms.

American College Testing

A standardized test used for college admissions in the United States that assesses a student's readiness for college-level work.

Margin of Error

A measure of the range of values below and above the sample statistic in a confidence interval within which the true population parameter is expected to lie.

Sample Mean

The mean of a set of samples, obtained by adding all the values together and then dividing by the total count of observations.