f(x)在x=2处连续,lim[f(x)/(x-2)]=3 (X趋向于2),求f(2)和f'(2)
问题描述:
f(x)在x=2处连续,lim[f(x)/(x-2)]=3 (X趋向于2),求f(2)和f'(2)
f(x)在x=2处连续,lim[f(x)/(x-2)]=3 (X趋向于2),求f(2)和f'(2)
答
3=lim[f(x)/(x-2)] (X趋向于2)=lim[f'(x)] (X趋向于2)=f'(2) 0/0型极限3=lim[f(x)/(x-2)] (X趋向于2)可得 1=limf(x)/[3(x-2)] (X趋向于2)因此 f(2)=lim[f(x)] (X趋向于2)=lim[3(x-2)] (X趋向于2)=0;...3=lim[f(x)/(x-2)] (X趋向于2)=lim[f'(x)] (X趋向于2)=f'(2) 0/0型极限如何得到这个?前面的等式是条件给出的,第二个等式是 0/0型 极限求导法则lim[f(x)/(x-2)] (X趋向于2) =lim[f'(x) / (x-2)' ] (X趋向于2)