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