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
望采纳
lim(x→0)(e^x-e^sinx)/(x-sinx)
x->0
分母
sinx~ x- (1/6)x^3
x-sinx ~ (1/6)x^3
分子
e^x ~ 1 + x + (1/2)x^2 + (1/6)x^3
e^(sinx)
~ e^(x- (1/6)x^3)
~1 + (x- (1/6)x^3) + (1/2)(x- (1/6)x^3)^2 + (1/6)(x- (1/6)x^3)^3
~ 1 +x +(1/2)x^2
e^x- e^(sinx) ~ (1/6)x^3
lim(x→0)(e^x-e^sinx)/(x-sinx)
=lim(x→0)(1/6)x^3/[ (1/6)x^3]
=1
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024