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lim{[(5x-4)^(1/2)-x^(1/2)]/(x-1)},在x→1时的值?
题目详情
lim{[(5x-4)^(1/2)-x^(1/2)]/(x-1)},在x→1时的值?
▼优质解答
答案和解析
(5x-4)^(1/2)-x^(1/2)
=[(5x-4)-x]/[(5x-4)^(1/2)+x^(1/2)]
=4(x-1)/[(5x-4)^(1/2)+x^(1/2)]
lim{[(5x-4)^(1/2)-x^(1/2)]/(x-1)}
=lim 4(x-1)/[(5x-4)^(1/2)+x^(1/2)]/(x-1)
=lim 4/[(5x-4)^(1/2)+x^(1/2)]
=4/(1+1)
=2
=[(5x-4)-x]/[(5x-4)^(1/2)+x^(1/2)]
=4(x-1)/[(5x-4)^(1/2)+x^(1/2)]
lim{[(5x-4)^(1/2)-x^(1/2)]/(x-1)}
=lim 4(x-1)/[(5x-4)^(1/2)+x^(1/2)]/(x-1)
=lim 4/[(5x-4)^(1/2)+x^(1/2)]
=4/(1+1)
=2
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