By Taylor's theorem, we can find a Taylor polynomial P 3
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(t) of degree 3 for the function g(t)=cos(2t)sin(4t) near t=0 such that g(t)=P 3
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(t)+R 3
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(0,t) in some interval where R 3
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(0,t) is the remainder term. Writing P 3
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(t) as P 3
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(t)=a 0
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+a 1
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t+a 2
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t 2
+a 3
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t 3
, calculate the coefficient a 3
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.