x→0求lim{lncos2x / lncos3x}以及lim(e^x - e^-x - 2x)/(x-sinx)求具体的解析
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x→0求lim{lncos2x / lncos3x}以及lim(e^x - e^-x - 2x)/(x-sinx)求具体的解析
x→0求lim{lncos2x / lncos3x}以及lim(e^x - e^-x - 2x)/(x-sinx)求具体的解析
x→0求lim{lncos2x / lncos3x}以及lim(e^x - e^-x - 2x)/(x-sinx)求具体的解析
x→0时,lim{lncos2x / lncos3x}=lim{ (lncos2x )' / (lncos3x)' }=lim{ 2tan2x / 3tan3x }=lim{ 4/9* (tan2x/2x)*(3x/tan3x }=4/9 ,因为 lim tanx/x =1 (x→0);
x→0时,lim(e^x - e^-x - 2x)/(x-sinx)=lim(e^x - e^-x - 2x)'/(x-sinx)' =lim(e^x + e^-x - 2)/(1-cosx)=lim(e^x + e^-x - 2)'/(1-cosx)' =lim(e^x -e^-x )/sinx =lim(e^x -e^-x )'/sinx ' =lim(e^x+e^-x )/cosx =2
1. 洛必达法则
lim(lncos2x/lncos3x)
=lim(2tan2x/3tan3x)
=2/3lim(2x/3x)无穷小替换
=4/9
2洛必达法则
lim(e^x+e^-x-2)/(1-cosx)
=lim(e^x+e^-x-2)/(1-cosx)
=lim (e^x-e^-x) /sinx
=lim e^-x (e^2x-1)/sinx
=lim e^-x *2x/x 无穷小替换
=2