Determine the first four non-zero terms of the Taylor series at x = 0 for f(x) = sin $x ^ { 3 }$ .
Is $f ( x ) = x ^ { 3 } + \frac { x ^ { 9 } } { 3 ! } + \frac { x ^ { 15 } } { 5 ! } + \frac { x ^ { 21 } } { 7 ! }$ the correct answer?

Question

Quizplus · Accepted Answer

The Taylor series of $f(x) = \sin(x^3)$ at $x = 0$ is given by $f(x) = x^3 - \frac{x^9}{3!} + \frac{x^{15}}{5!} - \frac{x^{21}}{7!} + \cdots$, which means the signs alternate between terms, unlike the series provided in the question.

Determine the First Four Non-Zero Terms of the Taylor Series x3x ^ { 3 }x3

Determine the First Four Non-Zero Terms of the Taylor Series $x ^ { 3 }$