设函数f(x)={arctan[1/(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
问题描述:
设函数f(x)={arctan[1/(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
答
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.