求极限 lim n->1 ((x^1/3-1)/(x^1/2-1))
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求极限 lim n->1 ((x^1/3-1)/(x^1/2-1))
求极限 lim n->1 ((x^1/3-1)/(x^1/2-1))
求极限 lim n->1 ((x^1/3-1)/(x^1/2-1))
用洛比塔法则
/lim_{x -> 1} ((x^1/3-1)/(x^1/2-1)) = /lim_{x -> 1} ((x^1/3-1)'/(x^1/2-1)') =
/lim_{x -> 1} (2 * x ^(-1/6) / 3) = 2 / 3
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...
全部展开
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
收起
lim n->1 ((x^1/3-1)/(x^1/2-1))
=lim n->1 [(1/3)*x^(-2/3)]//[(1/2)x^(-1/2)]
=lim n->1 [(2/3)*x^(1/2-2/3)]
=(2/3)*1^(-1/6)
=2/3
此极限值为4/3
matlab求解代码:
clear
syms x;
limit((x^1/3-1)/(x^1/2-1),x,1)
ans =
4/3