求极限lim(arcsinx*arctanx/2x^2)x趋近于0
问题描述:
求极限lim(arcsinx*arctanx/2x^2)x趋近于0
答
先看lim arcsinx/x设arcsinx=tx=sintx趋近于0,t也趋近于0lim arcsinx/x=lim t/sint=1再看lim arctanx/x设arctanx=t,x=tantx趋近于0,t也趋近于0cost趋近于1,t/sint趋近于1lim arctanx/x=lim t/tantlim cost*t/sint=1...