The function f(x) = sin(6x) has a Maclaurin series. Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with nonzero terms.
Added by Emily S.
Step 1
f(x) = sin(6x) f'(x) = 6cos(6x) f''(x) = -36sin(6x) f'''(x) = -216cos(6x) f''''(x) = 1296sin(6x) Now, we need to evaluate these derivatives at x = 0. f(0) = sin(0) = 0 f'(0) = 6cos(0) = 6 f''(0) = -36sin(0) = 0 f'''(0) = -216cos(0) = -216 f''''(0) = 1296sin(0) Show more…
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