求极限!分母为零!像lim h→0 ((1+h)^(1/2)-1)/h和lim x→-1 (x^2+2x+1)/(x^4-1)的,
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求极限!分母为零!像lim h→0 ((1+h)^(1/2)-1)/h和lim x→-1 (x^2+2x+1)/(x^4-1)的,
求极限!分母为零!
像lim h→0 ((1+h)^(1/2)-1)/h和lim x→-1 (x^2+2x+1)/(x^4-1)的,
求极限!分母为零!像lim h→0 ((1+h)^(1/2)-1)/h和lim x→-1 (x^2+2x+1)/(x^4-1)的,
第一题是
分子分母同时乘上 根号(1+h)+1,分子成了h,分母是h*(根号(1+h)+1),约去h,得
1/(根号(1+h)+1)
代入h=0,得1/2.
第二题
分子是(x+1)^2,分母是(x+1)(x-1)(x^2+1)
约去(x+1),则
分子是(x+1),分母是(x-1)(x^2+1)
代入x=-1,则
分子是0,分母是-4,得0
(x^2+2x+1)/(x^4-1) = (x+1)^2/(x^4-1)
显然有当x→-1时,分子(x+1)^2→0
故当x→-1时,极限为0