x→0
lim arctanx / x
换元t=arctanx
=lim(t→0) t / tant
=lim (cost)*(t / sint)
=1

lim (secx-1) / (x^2/2)
=lim (1-cosx)/cosx / (x^2/2)
=lim(2sin^2(x/2)) / (x^2/2) * (1/cosx)
=lim [sin(x/2) / (x/2)]^2 * (1/cosx)
=1
有不懂欢迎追问