f(x)=xarctan1⼀x(×不等于o)f(x)=0 (X=o时)求函数是否连续,是否可导。

2025-04-04 16:37:38
推荐回答(1个)
回答1:

lim(x->0) f(x)
=lim(x->0) x.arctan(1/x)
=0
= f(0)
=> x= 0 , f(x) 连续

f'(0)
= lim(h->0) [f(h) - f(0)] /h
= lim(h->0) [ harctan( 1/h) ] /h
= lim(h->0) arctan( 1/h)
=π/2