已知{limx趋近0 [（sin6x）+xf(x)]/x^3}=0 求limx趋近0 [6+f(x)]/x^2=?答案是36._数学解答

已知{limx趋近0 [（sin6x）+xf(x)]/x^3}=0 求limx趋近0 [6+f(x)]/x^2=?答案是36.

人气：340 ℃　时间：2020-07-24 01:58:41

解答

f有二阶导数吧?条件要写全了,否则很难做题的.Taylor展式最简单,sin6x=6x-(6x)^3/6+小o(x^3),xf(x)=x(f(0)+f'(0)x+f''(0)/2x^2+小o(x^2))=xf(0)+x^2f'(0)+0.5x^3f''(0)+小o(x^3),于是由条件知f(0)+6=0,f'(0)=0,.-36+0...