求极限当x→0若lim[sin6x+x f(x)]/x3=0,求lim[6+ f(x)]/x2

问题描述:

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

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→...