设函数f(x)={arctan[1⼀(x-1)],x不等于1,0,x=1 求:f(x)的极限,x趋于1减,和f(x)的极限,x趋于1加

2024-12-17 17:24:30
推荐回答(2个)
回答1:

x→1+时,1/(x-1)→+∞,arctan(1/(x-1)→π/2,lin(x→1+)f(x)=π/2,
x→1-时,1/(x-1)→-∞,arctan(1/(x-1)→-π/2,lin(x→1+)f(x)=-π/2.

回答2:

lim(x->1-)f(x)
=lim(x->1-){arctan[1/(x-1)]
= -π/2
lim(x->1+)f(x)
=lim(x->1+){arctan[1/(x-1)]
= π/2
lim(x->1)f(x) 不存在