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limx→0 5x%sin3x/tAn2x

用洛必达法则处理之,如上图,望采纳/

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(...

用等价无穷小,tan2x和sin3x等价于2x和3x.

等价替换适用于乘、除,不适用加减。当你学到泰勒公式之后,你就明白为什么。 (x→0)lim(tan3x-sin2x)/sin5x=(x→0)lim(tan3x-sin2x)/5x =(x→0)lim(3sex3x-2cos2x)/5=(x→0)lim(3-2)/5=1/5

解: X→ 0 tan2x/sin3x =2x/3x =2/3 极限为: 2/3

2/3

limx→0 tan(2x+x^3)/sin(x-x^2) =limx→0 (2x+x^3)/(x-x^2) =limx→0 (2+x^2)/(1-x) =(2+0)/(1-0) =2

x→0时2x+x^3→0 x-x^2→0 即tan(2x+x^3)→0 ,sin(x-x^2)→0 分子分母同时→0 适用于洛必塔法则 lim(x→0)[tan(2x+x^3)/sin(x-x^2)] =lim(x→0){[tan(2x+x^3)]'/[sin(x-x^2)] '} =lim(x→0){[sec(2x+x^3)]^2*(2+3x^2)]/[cos(x-x^2) *(1-2x)]} x→0,sec(2x+...

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

lim x→0,(tanx-sinx)/(sin2x)^3 应用罗比达法则,分子分母同时求导 上式=lim x→0,(1/(cosx)^2-cosx)/[3*(sin2x)^2*cos2x*2] =1/6lim x→0(1-(cosx)^3)/(sin2x)^2 再次应用罗比达法则,分子分母同时求导 上式=1/6lim x→0(3(cosx)^2*sinx)/2sin...

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