f(x)=ln(1-x^2)/1-cos(x/2)=?(x趋向于0)

问题描述:

f(x)=ln(1-x^2)/1-cos(x/2)=?(x趋向于0)

x趋向于0时,
ln(1-x^2)趋向于0
1-cos(x/2)趋向于0
运用洛必达法则,有
f(x)=lim{ln(1-x^2)/(1-cos(x/2))}=lim{[(-2x)/(1-x^2)]/[(1/2)sin(x/2)]}
此时x趋向于0时,lim(1-x^2)=1,lim[sin(x/2)]=x/2
因此f(x)=-4*lim[x/(x/2)]=-8