lim(x→1)3次根号x^2-2乘3次根号x+1/(x-1)^2
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lim(x→1)3次根号x^2-2乘3次根号x+1/(x-1)^2
lim{[x^(1/3)]^2-2*x^(1/3)+1}/(x-1)^2
(x→1)
=lim[(x^2)^(1/3)-2*x^(1/3)+1]/(x-1)^2
(x→1)
lim{[x^(1/3)]^2-2*[x^(1/3)]+1}/(x-1)^2
(x→1)
=lim[x^(1/3)-1]^2/(x-1)^2
(x→1)
=lim{[x^(1/3)-1]/(x-1)}^2
(x→1)
=lim{1/[x^(2/3)-x^(1/3)+1]}^2
(x→1)
=(1/1)^2
=1.
(x→1)
=lim[(x^2)^(1/3)-2*x^(1/3)+1]/(x-1)^2
(x→1)
lim{[x^(1/3)]^2-2*[x^(1/3)]+1}/(x-1)^2
(x→1)
=lim[x^(1/3)-1]^2/(x-1)^2
(x→1)
=lim{[x^(1/3)-1]/(x-1)}^2
(x→1)
=lim{1/[x^(2/3)-x^(1/3)+1]}^2
(x→1)
=(1/1)^2
=1.
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