求极限(x→0)(sinx-tanx)/(x^2(e^2x -1))

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求极限(x→0)(sinx-tanx)/(x^2(e^2x-1))求极限(x→0)(sinx-tanx)/(x^2(e^2x-1))求极限(x→0)(sinx-tanx)/(x^2(e^2x-1))先

求极限(x→0)(sinx-tanx)/(x^2(e^2x -1))
求极限(x→0)(sinx-tanx)/(x^2(e^2x -1))

求极限(x→0)(sinx-tanx)/(x^2(e^2x -1))
先用等价无穷小:e^(2x) -1 2x
原式 =lim (sinx - tanx) / (2x^3)
=lim [cosx - (secx)^2] / 6x^2 【罗比达法则】
=lim [(cosx)^3 -1] / [6x^2 (cosx)^2)]
=lim (cosx -1)[(cosx)^2 +cosx +1] / [6x^2 (cosx)^2) ]
=lim [(cosx)^2 +cosx +1] / [12 (cosx)^2 ] 【等价无穷小cosx -1 1/2 x^2】
= 1/4