大一高数题...help..lim(x一sinx)/(x+sinx)x→0

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大一高数题...help..lim(x一sinx)/(x+sinx)x→0
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大一高数题...help..lim(x一sinx)/(x+sinx)x→0
大一高数题...help..
lim(x一sinx)/(x+sinx)
x→0

大一高数题...help..lim(x一sinx)/(x+sinx)x→0
应用洛比达法则,分子分母的式子都求导变成
lim(1-cosx)/(1+cosx)=(1-1)/(1+1)=0
x→0
也可以用重要的极限,limsingx/x=1求,上下同除于x得
x→0
lim(1一sinx/x)/(1+sinx/x)
x→0
=(1-1)/(1+1)
=0

应用洛比达法则
lim(x一sinx)/(x+sinx)
x→0
= lim(1-cosx)/(1+cosx)=(1-1)/(1+1)=0
x→0

lim(sinx/x)=1
lim(x一sinx)/(x+sinx)
=lim(1一sinx/x)/(1+sinx/x)
=(1-1)/(1+1)
=0