Question

极限,(e^x-1-x)^2/x^3sinx x趋向于0

Answer 1

limx→0(e^x-1-x)^2/x^3sinx

=limx→0(e^x-1-x)^2/x^4*limx→0x/sinx

=[limx→0(e^x-1-x)/x^2]^2*1

=[limx→0(e^x-1)/2x]^2

=(limx→0e^x/2)^2

=(1/2)^2

=1/4.