lim(x趋向0)ex次方-e-x次方-2x|x-sinx等于?

题目

lim(x趋向0)ex次方-e-x次方-2x|x-sinx等于?

答案

lim(x趋向0)ex次方-e-x次方-2x|x-sinx 洛必达法则
=lim(x->0)(e^x+e^(-x)-2)/(1-cosx)
=lim(x->0)(e^x-e^(-x))/(sinx)
=lim(x->0)(e^x+e^(-x))/(cosx)
=(1+1)/1
=2