求极限lim(x→0)(根号下1+tanx减去根号下1+sinx)/sin^3x

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求极限lim(x→0)(根号下1+tanx减去根号下1+sinx)/sin^3x

求极限lim(x→0)(根号下1+tanx减去根号下1+sinx)/sin^3x
求极限lim(x→0)(根号下1+tanx减去根号下1+sinx)/sin^3x

求极限lim(x→0)(根号下1+tanx减去根号下1+sinx)/sin^3x
分子分母同时乘以(根号下1+tanx加根号下1+sinx),
则所求=lim(x→0)(tanx-sinx)/[sin^3x(根号下1+tanx加根号下1+sinx)]
=lim(x→0)(tanx-sinx)/(2sin^3x),分子分母除以sinx
=lim(x→0)(1/cosx-1)(2sin^2x)
=lim(x→0)(1-cosx)/(2sin^2x)用洛比达法则,分子分母同时求导
=lim(x→0)sinx/(4sinx cosx)
=lim(x→0)1/(4cosx)
=1/4