Question

求解极限

Answer 1

方法一：重要极限lim(x→0) (1+x)^(1/x)=e
lim(x→0) (1-2tanx)^(3cotx)
=lim(x→0) [1+(-2tanx)]^{(-1/2tanx)[3cotx*(-2tanx)]}
=e^lim(x→0)[3cotx*(-2tanx)]
=e^(-6)

方法二：
lim(x→0) (1-2tanx)^(3cotx)
=lim(x→0) e^ (3cotx)ln(1-2tanx)
=e^lim(x→0) 3ln(1-2tanx)/tanx
=e^lim(x→0) 3*(-2)x/x .....等价无穷小替换
=e^(-6)

Answer 2

lim(x->0)(1-2tanx)^cotx
=lim(x->0) [1+1/(-2cotx)]^[(-2cotx)/(-2)]
=e^(-1/2)
=1/√e

Answer 3

lim x-0 (1-2tanx)^3cotx
=lim x-0 (1-2tanx)^3/tanx
x趋近0 tanx~x
lim x-0 (1-2x)^3/x
=lim x-0 [(1-2x)^1/-2x]^-6
=e^-6

Answer 4

不好意思，都还给老师了已经。期待别人回答，我也学习下。

Answer 5

4524