f(x)在0點(diǎn)的左導(dǎo)數(shù)與有導(dǎo)數(shù)相等,均為x²*sin(1/x)的導(dǎo)數(shù),
即2xsin(1/x)-cos(1/x),當(dāng)x->0+時(shí)和x->0-時(shí),兩導(dǎo)數(shù)相等.
所以f(x)在0點(diǎn)可導(dǎo)
因?yàn)閒(x)在0點(diǎn)可導(dǎo),所以f(x)在0點(diǎn)連續(xù).
f(x)在x=1點(diǎn)處的左導(dǎo)數(shù)為（e的x次方）,將x=1代入得e,
f(x)在x=1點(diǎn)處的右導(dǎo)數(shù)為a/x,將x=1代入得a
由f(x)在點(diǎn)X=1處可導(dǎo)可知f(x)在x=1點(diǎn)處的左導(dǎo)數(shù)等于f(x)在x=1點(diǎn)處的右導(dǎo)數(shù)
即a=e
又f(1)+=f(1)-,所以b=e