lim┬x sin[x^3 ] [sinx]^2
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/10 11:16:26
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(tanx-sinx)/sin³x=(sinx/cosx-sinx)/sin³x=(1/cosx-1)/sin²x=[(1-cosx)/cosx]/(1-cos²
lim(tan^3(3x)/(X^2sin(2x))=(27/2)*lim{[tan^3(3x)/(3x)^3]*[2X/sin(2x)]}=27/2或用洛彼得法则
limx[sinln(1+3/x)-sinln(1+1/x)],x趋近于无穷大=lim[sinln(1+3/x)-sinln(1+1/x)]/(1/x)拆项sin(x)~xln(1+3/x)~3/x注
先看第一步tanx-sinx就是公式变形,sinx=tanx*cosx,然后代进去,tanx-tanx*cosxtanx(1-cosx),然后tanx等价于x,1-cosx等价于2x^2,sin^3x
limsin3x/tan5x=lim3cos3x/[5(sec5x)^2]=(3/5)limcos3x(cos5x)^2=(3/5)cos3π(cos5π)^2=-3/5limtanx/x=limx/
令a=π-x则a趋于0sin3x=sin(3π-3a)=sin3asin2x=sin(2π-2a)=-sin2a所以原式=-lim(a→0)sin3a/sin2asin3a和sin2a的等价无穷小是3
(1)sin2x5xsin2x2lim-------------------=lim--------------*lim------------*------=2/5x→0sin5xx→0sin5xx
令t=1\x原式=limt→0(3/t-1)/(1/t*sint^2)=limt→0(3/t-1)/(1/t*t^2)-----这里用到无穷小量有关知识=limt→0(3-t)=3
令t=arcsinx则x=sintx→0时t→0所以原式=(等价无穷小代换)lim(x-arcsinx)/x³=lim(sint-t)/sin³t=lim(sint-t)/t&su
1,lim(x→∞)(sinx/x+100)=0+100=1002,lim(x→∞)xtan(1/x)=lim(x→∞)tan(1/x)/(1/x)=lim(x→∞)(-1/x^2)sec²
由和差化积公式分子=2sin[(x^3+x^2)/2]cos[(x^3+x^2-2x)/2]x→0,则(x^3+x^2)/2→0,sin则(x^3+x^2)/2和(x^3+x^2)/2是等价无穷小而c
1.Maclaurin展开或者把分子化为:sinx(1-cosx)/cosx,其中sinx->x,(1-cosx)->x^2*(1/2),所以分子就是x^3*(1/2),结果为1/22.a^x用Mac
lim(x→0)(x-sin(3x))/(x+sinx)(这是0/0型,运用洛必达法则)=lim(x→0)(1-3cos3x)/(1+cosx)=-1
原式=lim(x->0)[(sinx/cosx-sinx)/sin³x]=lim(x->0)[(1-cosx)/(sin²xcosx)]=lim(x->0)[2sin²(
lim(x趋向于3)sin(x-3)/(x*x-9)=lim(x趋向于3)sin(x-3)/[(x-3)(x+3)]=[lim(x趋向于3)sin(x-3)/(x-3)]*[lim(x趋向于3)1/(
lim[sin(1/X)*sinX]=limX[sin(1/X)*sinX]/X=lim(sinX)/X*(sin(1/X)/(1/X)当X趋近无穷大时,lim(sin(1/X)/(1/X)=11/X
当x趋于0时,tanx-sinx=tanx*(1-cosx),而tanx等价于sinx,1-cosx等价于0.5(sinx)^2,那么tanx*(1-cosx)等价于0.5(sinx)^3所以lim(
=lime^sinx·(e^(tanx-sinx)-1)/x^3=1×lim(e^(tanx-sinx)-1)/x^3=lim(tanx-sinx)/x^3=lim(sinx/x)·lim(1/cos
原式=lim(x->0)sinx(secx-1)/x^3=lim(x->0)(secx-1)/x^2=lim(x->0)(1-cosx)/x^2cosx=lim(x->0)2sin^2(x/2)/x^