AP

MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let q(x)=(sin⁡x)2q(x)=(\sin x)^{2}. (1) Write the Maclaurin series for sin⁡x\sin x through the term containing x11x^{11}. (2) Form the product (sin⁡x)2(\sin x)^{2} using your series from part (a) and simplify to obtain all terms of degree less than or equal to 11. Show all algebraic steps used to combine like powers of xx. (3) Determine the exact coefficient of x10x^{10} in the Maclaurin series for q(x)q(x).

Related theory

Browse the problem library