求极限lim(x→1) (x^1/2-1)/(x^1/3-1) 不会打根号.
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求极限lim(x→1) (x^1/2-1)/(x^1/3-1) 不会打根号.
lim(x→1) (x^1/2-1)/(x^1/3-1)=
lim(x→1) (x^1/2-1)* (x^1/2+1)/ (x^1/2+1)((x^1/3-1)=
lim(x→1) (x-1)/ (x^1/2+1)(x^1/3-1)=
lim(x→1) (x-1)*(x^2/3+x^1/3+1)/ (x^1/2+1)(x^1/3-1)
*(x^2/3+x^1/3+1)/=
lim(x→1) (x-1)*(x^2/3+x^1/3+1)/ (x^1/2+1)(x-1)=
lim(x→1) (x^2/3+x^1/3+1)/ (x^1/2+1)=
(1+1+1)/(1+1)=
3/2
lim(x→1) (x^1/2-1)* (x^1/2+1)/ (x^1/2+1)((x^1/3-1)=
lim(x→1) (x-1)/ (x^1/2+1)(x^1/3-1)=
lim(x→1) (x-1)*(x^2/3+x^1/3+1)/ (x^1/2+1)(x^1/3-1)
*(x^2/3+x^1/3+1)/=
lim(x→1) (x-1)*(x^2/3+x^1/3+1)/ (x^1/2+1)(x-1)=
lim(x→1) (x^2/3+x^1/3+1)/ (x^1/2+1)=
(1+1+1)/(1+1)=
3/2
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