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Q41Section C (Section C)41 of 60

Taylor coefficients of 3 e^x cos 2x

Let f:R→Rf:\mathbb{R}\to\mathbb{R} be the function defined by f(x)=3excos⁡2xf(x)=3e^{x}\cos 2x. If p(x)=ax3+bx2+cx+dp(x)=ax^{3}+bx^{2}+cx+d is the third degree Taylor polynomial of ff at x=0x=0, then ∣a∣+∣b∣+∣c∣+∣d∣|a|+|b|+|c|+|d| equals __________ (in integer)

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