极限,(e^x-1-x)^2/x^3sinx x趋向于0

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极限,(e^x-1-x)^2/x^3sinx x趋向于0

极限,(e^x-1-x)^2/x^3sinx x趋向于0
极限,
(e^x-1-x)^2/x^3sinx x趋向于0

极限,(e^x-1-x)^2/x^3sinx x趋向于0
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.