帮我求下列极限:lim(x趋向于0)tan2x/sin5x;得有过程
问题描述:
帮我求下列极限:lim(x趋向于0)tan2x/sin5x;得有过程
答
lim(x->0)[tan(2x)/sin(5x)]
=lim(x->0){(2/5)*[tan(2x)/(2x)]*[(5x)/sin(5x)]}
=(2/5)*lim(x->0)[tan(2x)/(2x)]*lim(x->0)[(5x)/sin(5x)]
=(2/5)*1*1(应用重要极限lim(x->0)(sinx/x))
=2/5.