Mathematics

Problem

Let

q(x)=(\sin x)^{2}

. a. Write the Maclaurin series for

\sin x

through the term containing

x^{11}

. b. Form the product

(\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

x

. c. Determine the exact coefficient of

x^{10}

in the Maclaurin series for

q(x)

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