lim(1+3tan^2 x)^cot2x x趋向于0RT 求极限.我题目抄错了,不过原题我懂了
问题描述：
lim(1+3tan^2 x)^cot2x x趋向于0
RT 求极限.
我题目抄错了,不过原题我懂了
答
lim(1+3tan^2x)^cot2x
=lim(1+3tan^2x)^(3tan^2x/3tan^2x * cot2x)
=lim{(1+3tan^2x)^[1/(3tan^2x)]}^(cot2x * 3tan^2x)
=lim e^(cot2x * 3tan^2x)
=lim e^(3tan2x)
=lim e^0
=1