关于高等数学的几个问题求lim (arctanx/x) x趋向0lim sinx/(x^2*sin1/x) x-0lim (tanx-sinx)/x^2 x-0lim sinsinx^2/x^2 x-0要解答过程

Question

关于高等数学的几个问题
求lim (arctanx/x) x趋向0
lim sinx/(x^2*sin1/x) x-0
lim (tanx-sinx)/x^2 x-0
lim sinsinx^2/x^2 x-0
要解答过程

Answer 1

lim (arctanx/x) 1
lim sinx/(x^2*sin1/x) 无穷
lim (tanx-sinx)/x^2 0
lim sinsinx^2/x^2 1
1 4 实在没什么过程了.

第2题lim sinx/(x^2*sin1/x) = lim 1/x*sin1/x
sin1/x有界lim x*sin1/x=0所以lim 1/x*sin1/x=无穷
第3题 lim (tanx-sinx)/x^2 =lim (1/cosx - 1)/x
=lim (1-cosx)/xcosx = (x^2/2)/xcosx=0
用到了1-cosx ~x^2/2