lim[3/ 1-x^3+1/x-1]x→1

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 20:12:45
lim[3/ 1-x^3+1/x-1]x→1

lim[3/ 1-x^3+1/x-1]x→1
lim[3/ 1-x^3+1/x-1]
x→1

lim[3/ 1-x^3+1/x-1]x→1
lim[3/(1-x³) + 1/(x-1)]
=lim [ - 3/(x³-1) + (x²+x+1)/(x-1)(x²+x+1) ]
=lim (x²+x -2) / [(x-1)(x²+x+1)]
=lim (x-1)(x+2) / [(x-1)(x²+x+1)]
=lim (x+2)/(x²+x+1)
= 1

请将表达式写清楚，括号，谢谢

原式=lim{3(x-1)/[1-(x-1)^2*(x^2+x+1)]}
=lim{3(x-1)/[1-3(x-1)^2]}
=0

等于1

这样做3/1-x^3+1/x-1=3-(x^2+x+1)/1-x^3=-x^2-x+2/1-x^3=-(x-1)(x+2)/(1-x)(x^2+x+1)
=x+2/x^2+x+1
把x=1代入得极限为1

lim(x+e^3x)^1/x lim（x-3/x+1）^x lim趋向无穷大 lim x-1/x平方+3x-4 x-1 lim(x->0)((2-x)/(3-x))^1/x lim(x->无穷大){(2^x-3^x)/2}^(1/x) lim（ x→∞）（1+x / x)^3x lim(1-x)^3/x 求极限~ 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 极限函数计算lim( x^3 / sinx - x )lim( (1/e^x-1)-(1/x) ) lim(x趋近于1)x^3-1/x-1 lim(2x+3/2x+1)^(x+1) lim x->无限大 (1+1/2x) ^ 3x+lnx lim(2x-3/2x+1）^x+1 lim x-无穷 (√3x^2+1)/x+1 lim(x趋向于无穷)(1+3/x)^(x-3) lim(x→0)(1-3x)^(3/x) lim(1+3x)^3/x x趋向于0