Find the Maclaurin Polynomial of Degree 4 for the Function $$f ( x ) = e ^ { 9 x }$$

question 60

Multiple Choice

Find the Maclaurin polynomial of degree 4 for the function. $$f ( x ) = e ^ { 9 x }$$

• A) \(1 + 9 x + \frac { 81 } { 2 } x ^ { 2 } + \frac { 243 } { 2 } x ^ { 3 } + \frac { 2187 } { 8 } x ^ { 4 }\)
• B) \(1 - 9 x + \frac { 27 } { 2 } x ^ { 2 } + \frac { 243 } { 2 } x ^ { 3 } + \frac { 2187 } { 8 } x ^ { 4 }\)
• C) \(1 - 9 x + \frac { 27 } { 2 } x ^ { 2 } - \frac { 243 } { 4 } x ^ { 3 } + \frac { 2187 } { 16 } x ^ { 4 }\)
• D) \(1 + 9 x + \frac { 27 } { 2 } x ^ { 2 } + \frac { 243 } { 4 } x ^ { 3 } + \frac { 2187 } { 16 } x ^ { 4 }\)
• E) \(1 + 9 x + \frac { 81 } { 2 } x ^ { 2 } + \frac { 729 } { 4 } x ^ { 3 } + \frac { 2187 } { 2 } x ^ { 4 }\)

---

Definitions:

Treatment

An intervention or condition that experimenters apply to subjects or experimental units in a study to observe its effect.

Partial ANOVA Table

A simplified presentation of the results from an Analysis of Variance, showing selected sources of variation and their impact on a dependent variable.

Significance Level

The threshold below which a result is considered statistically significant, commonly used in hypothesis testing to determine if results can reject the null hypothesis.

ANOVA Table

A statistical table used to analyze the differences among group means in a sample.