求(e^x-e^sinx)/(x-sinx)的极限,x趋向0.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/12 01:43:28
![求(e^x-e^sinx)/(x-sinx)的极限,x趋向0.](/uploads/image/z/2449495-55-5.jpg?t=%E6%B1%82%28e%5Ex-e%5Esinx%29%2F%28x-sinx%29%E7%9A%84%E6%9E%81%E9%99%90%2Cx%E8%B6%8B%E5%90%910.)
x){I#5B7583BS_Bx>ټƗ3'TtD="}ِnCNfFţI
X"*6* IVhVJ:]4%6yvPـ9O?ӏ
-
|M4EkRqF0 C) m# X1n6RCM-CM}Cw
求(e^x-e^sinx)/(x-sinx)的极限,x趋向0.
求(e^x-e^sinx)/(x-sinx)的极限,x趋向0.
求(e^x-e^sinx)/(x-sinx)的极限,x趋向0.
lim(x→0) (e^x-e^sinx)/(x-sinx)
=lim(x→0) e^x[1-e^(sinx-x)]/(x-sinx)
=lim(x→0) [1-e^(sinx-x)]/(x-sinx)
=lim(x→0) -(sinx-x)/(x-sinx)
=1
原式=lim(x→0)(e^x-cosx*e^sinx)/(1-cosx)=lim(x→0)(e^x+(sinx-cos^2(x))e^sinx)/sinx=lim(x→0)(e^x+(cosx+2cosxsinx+sinxcosx-cos^3(x))e^sinx)/cosx=(1+(1-1)*1)/1=1