若x^2-y^2=1,则1/x^2+2y/x的范围是用三角换元的方法做,
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若x^2-y^2=1,则1/x^2+2y/x的范围是用三角换元的方法做,
若x^2-y^2=1,则1/x^2+2y/x的范围是
用三角换元的方法做,
若x^2-y^2=1,则1/x^2+2y/x的范围是用三角换元的方法做,
∵x^2-y^2=1,
令x=secθ,y=tanθ,θ∈[0,2π],
且θ不等于π/2,3π/2,则
w=1/(secθ)^2+2tanθ/secθ
=-(sinθ-1)^2+2
当θ∈[0,π/2)时,w∈[1,2)
当θ∈(π,3π/2)时,w∈(-2,1)
当θ∈(3π/2,2π]时,w∈(-2,1]
∴w的取值范围为:-2
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