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lim sin2x 3x

limsin2x/3x(X趋近于0) 因为当X趋近于0时,sin2x等价于2X 所以limsin2x/3x(X趋近于0)=2x/3x=2/3

2011-12-04 lim sin2x/3x x趋向0 3 2013-01-12 lim(x趋向于0)f(x)/x=2 则lim(x趋向于0)... 2014-06-07 lim(sin2x)/(x^3+3x) x趋向于0 ...

分子分母同时除以x 原式=lim(x~0)【1-(sin2x/x)】/【1+tan3x/x】 =(1-2)/(1+3) =-1/4

x→0则2x→0,3x→0 所以sin2x和2x是等价无穷小 tan3x和3x是等价无穷小 所以原式=lim(x→0)(2x/3x)=2/3

lim [sin(2x)/3x] x→0 =(2x)/(3x) =2/3 lim(1+ 3/x)^x x→∞ =lim[(1+ 3/x)^(x/3)]³ x→∞ =e³ lim [1- 1/(2x)]^x x→∞ =lim {[1+ 1/(-2x)]^(-2x)}^(-½) x→∞ =e^(-½) =√e/e

lim(sin2x/sin3x) =lim(xsin2x/xsin3x) =lim2/3(3xsin2x/2xsin3x) =lim2/3(sin2x/2x)/(sin3x/3x) =2/3lim(sin2x/2x)/lim(sin3x/3x) =2/3

解: 利用x→0时,sinx~x lim【x→0】(sin2x)/(3x) =lim【x→0】 (2x)/(3x) =2/3

lim(x→0)(sinx-xcosx)/(sin^3x)=lim(x→0)[(sinx-xcosx)]'/(sin^3x)'=lim(x→0)(cosx-cosx+xsinx)/[3(sin^2x)cosx]=lim(x-0) x/[3(sinxcosx)]=lim(x-0) x/[3sin(2x)/2]=lim(x-0) x'/[3sin(2x)/2]'=lim(x-0) 1/[3cos(2x)]=1/3

如图,主要思想是有界函数除以无解函数极限为0

泰勒公式。。。把上面和下面展开系数一除,结果出来了

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