lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 20:12:12

lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3
lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3

lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3
令t=x-1,则t→0
lim【x→1】{[x^(3x-2)-x]·sin2(x-1)}/(x-1)³
=lim【t→0】{[(t+1)^(3t+1)-(t+1)]·sin2t}/t³
=lim【t→0】{[(t+1)^(3t+1)-(t+1)]·2t}/t³
=2lim【t→0】[(1+t)^(3t+1)-1-t]/t² →利用等价无穷小代换x→0时,(1+x)^a-1~ax
=2lim【t→0】[t(3t+1)-t]/t²
=2lim【t→0】3t²/t²
=2×3
=6

用无穷小等量代换

lim(x→1)(x^3-3x+2)/(x^3-x^2-x+1) lim(x→1)[(x^(3x-2)-x)sin2(x-1)]/(x-1)^3 lim x→∞(2x+1)/(3x-4) lim(x→0)2x^3-x+1 lim((√1+x^2)+x)/((√x^3+x)-x)x→+无穷大求lim(x→0)x cos 1/x lim(x→∞)x^2/ (3x-1)的极限 lim x→1 x-1/x^2-x Lim [x^2/(x^2-1)]^x (x→∞) lim（ x→∞）（1+x / x)^3x lim(1+x/x)2x (x→∞) lim(x→0)e^x-x-1/x^2 lim(x->无穷大){(2^x-3^x)/2}^(1/x) lim(x->0)((2-x)/(3-x))^1/x lim(x→∞)(4x^3+2x-1)/(2x^3-3x+1) lim(x→∞)(2x^3-x^2-3)/(x^3-x+1) lim(x→∞)[（x^3+x^2+x^1+1)^(1/3) - x] 的极限. lim(x→0)[(1+X)(1+2X)(1+3x)-1]/x lim x→1 (x^2-4x+3)/(x^4-4x^2+3)