ans

14996
$\{0,1\}$

14997
$-\dfrac 12+\dfrac 32\mathrm{i}$

14998
$40\pi$

14999
$270$

15000
$0.1$

15001
$2$

15002
$\dfrac 12$

15003
$\dfrac{4\sqrt{6}}{25}$

15004
$2\sqrt{2}-1$

15005
$[\dfrac{5\pi}6,\dfrac{11\pi}6)$

15006
$\dfrac 14$

15007
$(1,3]$

15008
B

15009
A

15010
D

15011
D

15012
(1) $\dfrac{121}9$; (2) $S_n$的最大值为$3$, 当且仅当$n=2$或$3$时取得

15013
(1) 证明略; (2) $\dfrac{\sqrt{6}}6$

15014
(1) $\dfrac{41}{42}$; (2) $\dfrac{12}{5}>\dfrac{116}{75}$, 故应该先答人文历史题, 再答地理环境题

15015
(1) $\dfrac{\sqrt{6}}3$; (2) $\dfrac 43$或$\dfrac{4\sqrt{6}}9$; (3) 存在, $P$的坐标为$(1,1)$

15016
(1) $O(0,0)$是的, $A(2,0)$不是; (2) 证明略; (3) $\{(a,b)|b=-a\text{或}b=a^3-a, \ a\ne 0\}$