求极限x趋近于无穷,lim(x^2*arcsin1/x)/4x-1

题目

求极限x趋近于无穷,lim(x^2*arcsin1/x)/4x-1
要求用罗比达法则解、、亲们~

答案

lim(x^2*arcsin1/x)/4x-1,x→∞,1/x→0,等价无穷小代换,1/x→0,1/x~sin(1/x),arcsin1/x→1/x,则lim(x^2*arcsin1/x)/4x-1=limx/4x-1=1/4.