Lim [x^2/(x^2-1)]^x (x→∞)
来源：学生作业帮助网 编辑：六六作业网 时间：2025/01/31 03:57:31
Lim[x^2/(x^2-1)]^x(x→∞)Lim[x^2/(x^2-1)]^x(x→∞)Lim[x^2/(x^2-1)]^x(x→∞)lim[x^2/(x^2-1)]^x(x→∞)=lim1/[(
Lim [x^2/(x^2-1)]^x (x→∞)
Lim [x^2/(x^2-1)]^x (x→∞)
Lim [x^2/(x^2-1)]^x (x→∞)
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
取对数：原式=e^(x*lnx^2/x^2-1)
又因为：x*lnx^2/x^2-1=x(lnx^2-lnx^2-1)
然后用罗比达法则求导。
lim(1-x)^(2/x) x->0
lim(x^2+1/x^2-2x)^x=?
lim(x->无穷大){(2^x-3^x)/2}^(1/x)
Lim [x^2/(x^2-1)]^x (x→∞)
Lim(x>1) x-1/x^2+x-2.计算
lim x→1 x-1/x^2-x
极限：lim(x->2)1/(x-2)
lim x->正无穷大 x ( sqrt(x^2+1)-x )
lim(x->0)((2-x)/(3-x))^1/x
lim(1+x/x)2x (x→∞)
lim(x→0)e^x-x-1/x^2
lim(x+1/x+2)^x=?x趋于无穷
lim(x趋于无穷)(x/1+x)^(x+2)=?
lim(1-(5/x))^x-2
lim(x+e^2x)^(1/sinx)
lim(x(sin)^2)
1.lim x->∞ （2x/x^2+1)*cosx 2..lim x->∞{ [(x^2-x)arctanx]/x^3-x-5}3..lim x->0 （e^x-e^-x-2x)/(x-sinx) 4..lim x->0 (sinx-x)/(x^3) 5..lim x->0 (x^2*tanx)/(x-tanx) 6..lim x->0 (1+3/x)^2x 7..lim x->0 (1+2x)^(3/sinx) 8.lim x->∞ (x/1+x)^(x-3) 9..li
lim(x+1)^x+1(x+3)^x+3/x^2x+4 x趋于无穷