由y=(x+2)/[1+√(1-x²)]+[1-√(1-x²)]/x,
由-1<x<1,
设x=sint,-π/2<t<π/2
y=(sinx+2)/(1+cost)+(1-cost)/sint
=(sin²t+2sint+1-cos²t)/sint(1+cost)
=(2sint+2)/(1+cost)
(1)当t=-π/4,ymin=4-3√2
(2)当t=π/4,ymax=3√2/2.
由y=(x+2)/[1+√(1-x²)]+[1-√(1-x²)]/x,
由-1<x<1,
设x=sint,-π/2<t<π/2
y=(sinx+2)/(1+cost)+(1-cost)/sint
=(sin²t+2sint+1-cos²t)/sint(1+cost)
=(2sint+2)/(1+cost)
(1)当t=-π/4,ymin=4-3√2
(2)当t=π/4,ymax=3√2/2.