Question

求极限 题 求详解！！！！！

求极限1. x->0^-(负零) lim(2^1/x-1)/(2^1/x+1)
2.x->正无穷 lim sin{arctanx}
3.x->正无穷lim arccos[根号(x^2+x)-x]

Answer 1

1. lim 2(^1/x-1)/(2^1/x+1)=(0-1)/(0+1)=-1
2. lim sin(arctanx)=sin lim(arctanx)=sinπ/2=1
3. 原式=lim arccos(x/(√(x^2+x)+x))
=lim arccos(1/(√(1+1/x^2)+1))
=arccos(1/2)
=π/6