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)

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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)

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)
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)

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)
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;

∵f(x)/x-2=2,∴f(x)/x=4,对等号两边同时取当x→2时的极限:lim[f(x)/x]=lim4,代入得limf(x)/2=4,即f(2)/2=4,∴f(2)=8,∴f'(2)=0

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