(sinx^3+tanx-sinx)/ln(1+x^3)x趋近于0的极限
问题描述:
(sinx^3+tanx-sinx)/ln(1+x^3)x趋近于0的极限
答
x-0,
ln(1+x^3)-x^3,
然后上下求导,原式=[3x^2sinx^3cosx^3+(secx)^2-cos
x]/3x^2
=sinx^3cosx^3+1/(cosx)^2*[(1-cosx)*(1+cosx+(cosx)^2)]/3x^2
=0+1*[1/2x^2*(1+1+1)]/3x^2
=1/2
好久没做极限了,也不知道对不对....
对了就采纳吧
答
=lim (sinx^3+tanx-sinx)/(x^3) 【等价无穷小代换】=lim (sinx^3 )/(x^3) + lim (tanx-sinx)/(x^3) 【因为按+分开后两部分极限都存在,故可以分开】=lim (x^3 )/(x^3) + lim (sinx / cosx -sinx)/(x^3) 【等价无穷小...