(e^x-e^tanx)/x(tanx)^2的极限当x趋向于0

来源:学生作业帮助网 编辑:六六作业网 时间:2024/07/07 08:49:40
(e^x-e^tanx)/x(tanx)^2的极限当x趋向于0(e^x-e^tanx)/x(tanx)^2的极限当x趋向于0(e^x-e^tanx)/x(tanx)^2的极限当x趋向于0lim(x→0

(e^x-e^tanx)/x(tanx)^2的极限当x趋向于0
(e^x-e^tanx)/x(tanx)^2的极限当x趋向于0

(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