求极限当x→0若lim[sin6x+x f(x)]/x3=0,求lim[6+ f(x)]/x2
若lim[sin6x+xf(x)]/x3=0,求lim[6+ f(x)]/x2
x→0 x→0
人气：421 ℃ 时间：2019-08-17 23:15:49
解答
利用sinx的麦克劳林公式展开 sin6x=6x-(6x)^3/3!+o(x^3） f(x)在x=0处展开f(x)=f(0)+f'(0)x+1/2f''(0)x^2+o(x^2) 代入得到 lim[sin6x+xf(x)]/x^3=6x-(6x)^3/3!+o(x^3)+f(0)x+f'(0)x^2+1/2f''(0)x^3+o(x^3)/x^3=0 x→...
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