lim [∫(0,x) t/(1+t)^(1/2)dt] / (tanx)^2
当x趋于0时,该极限为0/0型
根据L'Hospital法则
=lim (x/(1+x)^(1/2)) / (2*tanx*(1/cos^2x))
=lim (x*cos^2x) / (2*(1+x)^(1/2)*tanx)
=lim cos^2x / (2(1+x)^(1/2)) *lim x / tanx
=(1/2)*lim x/sinx * lim cosx
=1/2
有不懂欢迎追问