81导数的概念 f-(0)=lm-x3-0=0得f(0)=0 f(x)=/3x2 ≥0 (2)当x>0时,f(x)=1,当x<0时,f(x)=0 当x=0时f+(0)=mx+1-1=1 f(0)=lin1-y0,于f,(0)≠厂(0), 所以,f(x)在x=0不可导,故f(x)= 1,x>0 0,x<0 8.设函数f(x)= sin,z≠0 (m为正整数) 0 试问:(1)m等于何值时,f在x=0连续; (2)m等于何值时,f在x=0可导 (3)m等于何值时,f在x=0连续. 解(1)当m为任意正整数时,都有lmx"m1=0=f(0) 因此,当m为任意正整数时,f在x=0连续 (2)当m为大于1的正整数时,有linf(x)-f(0) mnxm-in1=0这时,∫在x=0处可导,且f(0)=0 当m=1时 limrm-Isin1不存在故∫在x=0不可导 (3)当m为大于2的正整数时,若x≠0,则 trams 1 nisin limf(r)=limzm-2(mzsin I )=0=f(0).故f在x=0 连续