limx→0{(tanx-x)/x^3}
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limx→0{(tanx-x)/x^3}
limx→0{(tanx-x)/x^3}
limx→0{(tanx-x)/x^3}
lim(x→0){(tanx-x)/x^3}
=lim(x→0{(tanx-x)'/(x^3)'
=lim(x→0{(1/cosx^2-1)'/(3x^2)'
=lim(x→0) (2sinx/cosx^3)/6x]
=(1/3)lim(x→0[(sinx/x)(1/cosx^3)
=1/3
洛必达法则,分子导数是sec^2x-1,分母是3x^2,化简为lim(1-cos^2x)/(3x^2)lim1/cos^2x=lim 2cosxsinx/6x*1=1/3
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