Find the first four nonzero terms in the Maclaurin series for the function.
-sin x cos x
A) $x - \frac { 1 } { 6 } x ^ { 3 } + \frac { 1 } { 30 } x ^ { 5 } - \frac { 2 } { 315 } x ^ { 7 } + \ldots$
B) $x - \frac { 2 } { 3 } x ^ { 3 } + \frac { 2 } { 15 } x ^ { 5 } - \frac { 4 } { 315 } x ^ { 7 } + \ldots$
C) $1 + x - \frac { 1 } { 2 } x ^ { 2 } - \frac { 1 } { 6 } x ^ { 3 } + \ldots$
D) $x + \frac { 1 } { 3 } x ^ { 3 } - \frac { 2 } { 15 } x ^ { 5 } + \frac { 4 } { 315 } x ^ { 7 } + \ldots$

Question

Find the first four nonzero terms in the Maclaurin series for the function.
-sin x cos x 
A) $x - \frac { 1 } { 6 } x ^ { 3 } + \frac { 1 } { 30 } x ^ { 5 } - \frac { 2 } { 315 } x ^ { 7 } + \ldots$
B) $x - \frac { 2 } { 3 } x ^ { 3 } + \frac { 2 } { 15 } x ^ { 5 } - \frac { 4 } { 315 } x ^ { 7 } + \ldots$
C) $1 + x - \frac { 1 } { 2 } x ^ { 2 } - \frac { 1 } { 6 } x ^ { 3 } + \ldots$
D) $x + \frac { 1 } { 3 } x ^ { 3 } - \frac { 2 } { 15 } x ^ { 5 } + \frac { 4 } { 315 } x ^ { 7 } + \ldots$

Quizplus · Accepted Answer

The Maclaurin series for sin x is $x - \frac{x^3}{6} + \frac{x^5}{120} - \frac{x^7}{5040} + \ldots$ and for cos x is $1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720} + \ldots$. Multiplying these series and collecting terms gives the series for sin x cos x as $x - \frac{2}{3}x^3 + \frac{2}{15}x^5 - \frac{4}{315}x^7 + \ldots$.

Find the First Four Nonzero Terms in the Maclaurin Series x−16x3+130x5−2315x7+…x - \frac { 1 } { 6 } x ^ { 3 } + \frac { 1 } { 30 } x ^ { 5 } - \frac { 2 } { 315 } x ^ { 7 } + \ldotsx−61​x3+301​x5−3152​x7+…

Find the First Four Nonzero Terms in the Maclaurin Series $x - \frac { 1 } { 6 } x ^ { 3 } + \frac { 1 } { 30 } x ^ { 5 } - \frac { 2 } { 315 } x ^ { 7 } + \ldots$