limx趋近于64x/(x-6)2

limx趋近于0sin3x/2xlim(x→0)sin3x/2x=lim(x→0)(sin3x/3x)*(3/2)=lim(3x→0)(sin3x/3x)*(3/2)lim(x→0)sinx/x=1=3/2利用两个重要极限，等于3/2。需要

证明limx趋近于0,y趋近于0x^3y/x^6+y^2不存在令y=kx^3,则极限=limkx^6/(x^6+k^2*x^6)=k/(1+k^2),由于此极限值和k有关,即(x,y)沿y=kx^3中不同路径趋于(0,0)时极限不相等,不符

limx^2/2-xx趋近于2分子是4,分母是0,因此极限是∞原式=lim(x-

limx趋近于01-gen1+x^2/x^2原式=[1+√(1+x^2)][1-√(1+x^2)]/x^2[1+√(1+x^2)]分子平方差=(1-1-x^2)/x^2[1+√(1+x^2)]=-x^2/x^2[1+√(1+x^2)]=-1

limx趋近于0(sinx/x)^(1/x^2)若看不清楚,可点击放大.

limx趋近于0(e^2x)-1/x  

limx趋近于3,x/(x^2-9)求极限极限不存在要极限存在必须左右极限相等limx->3-x/[(x-3)(x+3)]=-无穷,因为分母是趋向0-,3/0-->-无穷limx->3+x/[(x-3)(x+3)]=+无穷,因为分母是趋向0

limx趋近于1sin(1-x^2)/1-x=limx趋近于1cos(1-x^2)*(-2x)/(-1)=cos0*(-2)/(-1)=1*(-2)/(-1)=2所以0/0型,分子分母分别求导再数来计算limsin(1-x^2)/(1-x)

limx趋近于派(x-派)tanx/2是limx趋近于派(x-派)tan(x/2)正无穷

证明limx^2-6x+5/x-5=-4,x趋近于-3lim{(x²-6x+5)/(x-5)}=(x²-6x+5)/(x-5)=(3²+6*3+5)/(-3-5)=42/(-8)=-4；或lim{(x²

limx趋近于无穷x^2(π/2-arctan3x^2)设π/2-arctan3x^2=tx^2=(1/3)tan(π/2-t)=(1/3)cost/sintlimx趋近于无穷x^2(π/2-arctan3x^2)=(Limt趋近于0)(t

limx趋近于派(x-派)tanx/2的极限

limx趋近于0(e^2x-1)/sin4xlim(x->0)(e^2x-1)/sin4x(0/0)=lim(x->0)2e^2x/(4cos4x)=2/4=1/2

limx趋近于1,(1-x^2)/sinxlim(1-x^2)/sinx=0/sin1=0.lim(1-x^2)/sinπx=lim-2x/(πcosπx)=2/π

limx趋近于无穷(2-1/x+1/xx)

limx趋近于0时2arcsinx/3x

limx趋近于0,2arcsinx/3x=arcsinx~x原式=lim(2x/3x)=2/3

limx趋近于1x^2-1/inx答：lim(x→1)(x^2-1)/lnx=lim(x→1)(x-1)(x+1)/lnx=lim(x→1)(1+1)*(x-1)/lnx=lim(x→1)2(x-1)/lnx=lim(x→1)2/(1/x)

limx趋近于0tan2x分之x解利用等价无穷小x→0tan2x→2xlimx趋近于0(x/tan2x)=limx趋近于0(x/2x)=1/2利用等价无穷小替换tanx~x，题中为tan（2x）~2x，所以limx趋近于0tan2x分之x=

limx趋近于0lnsinx/xlim(sinx/x)=1y=lnu在u=1处连续limln(sinx/x)=ln1=0