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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

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

三分之四

ln(1+x)~x(x->0) 所以ln(1-3x)~-3x(x->0)

答: lim(x→0) sin(2x) / tan(3x) =lim(x→0) sin(2x) cos(3x) / sin(3x) =lim(x→0) sin(2x) / sin(3x) =lim(x→0) 2x /(3x) =2/3

泰勒公式。。。把上面和下面展开系数一除,结果出来了

=lim(sin3x+2xcos3x)/cos3x(sin2x+3x) =lim(3sin3x/3x+2cos3x)/cos3x(2sin2x/2x+3) =(3+2)/1(2+3)=1

lim(x->0) sin(2x)/tan(3x)=lim(x->) (2x)/(3x)=2/3 lim(x->0) sin(2x)/tan(3x)=lim(x->0) [sin(2x)]'/[tan(3x)]' =lim(x->0) 2cos(2x)/[3/cos^2(3x)]=2/3 lim(x->0) sin(2x)/tan(3x)=lim(x->0) sin(2x)cos(3x)/sin(3x) =lim(x->0) [sin(2x)cos(...

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