lim x趋于2 (x^2- 1)/x - 2 这个极限为什么是无穷大?

如果是选择题的话,只能选无穷,因为这是最接近的说法.如果是解答题的话,的确如您所说应该对趋近方向进行分类讨论,分别求出其左右极限才是正确的解答.用“无穷”来回答是不严谨的.

求极限x趋于无穷,Lim(1 - 2/x)^x 帮解一下这个谢谢

这个我不太在行,我的解法是 lim x->∞ (1-2/x)^x=lim x->∞ [1+(-2)/x]^[-2*x/(-2)]=lim x->∞ [1+(-2)/x]^[(x/(-2)]*(-2)=e^(-2)=1/e^2 但不知是不是这个答案

求极限lim(x→1) (x - 1)/(x∧2 - 1)

lim[x/(x-1)-2/(x^2-1)] =lim[x(x+1)-2]/(x^2-1) =lm(x^2+x-2)/(x^2-1) =lim(x+2)(x-1)/[(x+1)(x-1)] =lim(x+2)/(x+1) =3/2

求极限lim(x→∞)(1 - 2/x)^x

lim(x→∞)(1-2/x)^x = [lim(x→∞)(1-2/x)^(-x/2)]^(-2)=e^(-2)

Lim [x^2/(x^2 - 1)]^x (x→∞) 详细过程

lim [x^2/(x^2-1)]^x (x→∞) =lim1/[(1-x^(-2))^x]=lim1/[(1-1/x)^x*(1+1/x)^x]=lim1/[(1-1/x)^x]*lim1/[(1+1/x)^x]=1/lim[(1-1/x)^x]*1/lim[(1+1/x)^x]=1/e^(-1)*1/e^1=1

lim→∞ (2x^2+x - 1)/(x^2 - 1)求极限

解:lim (2x²+x-1)/(x²-1)x→∞=lim (2+ 1/x -1/x²)/(1- 1/x²)x→∞=(2+0-0)/(1-0)=2/1=2

lim(1 - 2/x)^x/2+1(x趋向于无穷)求极限

lim(1-2/x)^x/2+1x→∞=lim(1-2/x)^(-x/2)(-1)+1x→∞=1/e+1

limx→ 无穷〔x^2+x(x^2+2)^1/2〕

x→+∞时,x²+x√(x²+2)→+∝x→-∝时,lim[x²+x√(x²+2)]=lim{[x⁴-x²(x²+2)]/[x²-x√(x²+2)]}=lim{-2x²/[x²-x√(x²+2)]}=-2/lim[1+√(1+2/x²)]=-2/(1+1)=-1

limx趋于无穷(x - (x^2 - 1))

x→+∞lim[x-√(x²-1)]=lim{[x²-(x²-1)]/[x+√(x²-1)]=lim{1/[x+√(x²-1)]}=0如果x→-∞,x-√(x²-1)→-∞.

求lim x→+无穷 根号(x^2+1)/x+1

(x^2+1)/(x+1)=(x+1)+2/(x+1)-2=(x-1)+2/(x+1)当X趋向正无穷时,(x-1)趋向正无穷,而2/(x+1)趋向0,因为正无穷+0=正无穷.所以根号下正无穷=正无穷