(e^x-e^tanx)/x(tanx)^2的极限当x趋向于0

lim(x→0) (e^x-e^tanx)/x(tanx)^2
=lim(x→0) e^x[1-e^(tanx-x)]/x^3
=lim(x→0) [1-e^(tanx-x)]/x^3
=lim(x→0) (x-tanx)/x^3
=lim(x→0) (1-sec^2x)/(3x^2)
=lim(x→0) (-tan^2x)/(3x^2)
=-1/3