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MacLaurin Expansion of sin2x

A detailed description of how to find the first three nonzero terms of the Maclaurin expansion of the function f(x)=sin2x is given.

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Solution Preview

Remember that the Taylor series expansion of a function f(x) is equal to

f(a) + f'(a)(x-a) + [f''(a)(x-a)^2]/2! + ...

In the MacLaurin series expansion, a=0, so the first three terms are

f(0) + f'(0)x + [f''(0)x^2]/2!

f(0) = sin(2 x 0) = sin(0) = 0. This ...

Solution Summary

In this solution, we find the first three nonzero terms of the MacLaurin series expansion for the given function.

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