設函數f(x)={arctan[1/(x-1)],x不等於1,0,x=1求:f(x)的極限,x趨於1减,和f(x)的極限,x趨於1加

設函數f(x)={arctan[1/(x-1)],x不等於1,0,x=1求:f(x)的極限,x趨於1减,和f(x)的極限,x趨於1加

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