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
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/17 20:04:57
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.
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+0.5f''(0)=0,f(0)=-6,f'(0)=0,f''(0)=72,(6+f(x))/x^2=【6+f(0)+xf'(0)+0.5x^2f''(0)+小o(x^2)】/x^2=36+小o(1),极限是36
f(0)+6=0,f'(0)=0,.-36+0.5f''(0)=0,f(0)=-6,f'(0)=0,f''(0)=72,(6+f(x))/x^2=【6+f(0)+xf'(0)+0.5x^2f''(0)+小o(x^2)】/x^2=36+小o(1),极限是36
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
已知limx趋近0 [6+f(x)]/x^2=36,求limx趋近0 [(sin6x)+xf(x)]/x^3=?
已知limx趋近于[6sinx-(tanx)f(x)]/x^3=0 求limx趋近于0[6-f(x)]/x^2
已知limx/f(4x)=1,求limf(2x)/x x趋近0
lim(x趋近于0)[sin6x+xf(x)]/x^3=0,则lim(x趋近于0)[6+f(x)]/x^2=?
limx趋近于0 x/f(3x)=2,limx趋近于0 f(2x)/x=
limx趋近于0sin3x/2x
limx趋近0 x-sinx/x^2 =limx趋近0 1-cosx/2x 这一步是怎么转换过来的.
limx趋近于0时2arcsinx/3x
limx趋近于0 x2/sin2(x/3)
x趋近0时,lim(6x-sin6x)/x的3次方=?
limx趋近于0(sinx/x)^(1/x^2)