ans
004353
$[1,2)$

004270
$(-3,1]$

004254
$3$

004145
$1$

004083
$3$

004232
$\dfrac{34}{35}$

004216
$4$

004149
$[-\dfrac 12,1]$

004172
$\dfrac 12$

004089
$-1$与$\dfrac 12$

004415
$1$

004135
D

004136
C

031282
A

004159
(1) $2$; (2) $\arctan\dfrac{\sqrt{2}}4$

004442
(1) $\dfrac{\pi}{12}$或$\dfrac\pi 4$; (2) $\omega = \dfrac 23$, 单调递增区间为$[0,\dfrac\pi 2]$

004721
(1) $8\sqrt{3}-8$; (2) 当$A$在弧$\overset\frown{MN}$的四等分点(更靠近$M$)处时, 矩形$ABCD$的面积最大, 最大面积为$16\sqrt{2}-16$

004246
(1) $[0,\arctan\dfrac 32)\cup (\dfrac{3\pi}4,\pi)$; (2) $\dfrac 83\pi+\sqrt{3}$; (3) 曲线$C$的方程为$x^2=\begin{cases} 24-8y, & y\ge 0, \\ 24+12y, & y\le 0,\end{cases}$ $a$的取值范围为$(6,24)$

004352
(1) $-5,-3,-1,1,3,5,7$; (2) $a_n=\begin{cases}\dfrac {n+1}2, & n=2k-1,\\ 1-\dfrac n 2, & n = 2k \end{cases}$($k$为正整数); (3) 证明略

031311
$\{4,5\}$

031312
$(1,11)$

031313
$-\dfrac 35+\dfrac 45\mathrm{i}$

031314
$1$

031315
$2\sqrt{3}$

031316
$2$

031317
$(-\dfrac 15,\dfrac 25)$

031318
$(1,5)$

031319
$\dfrac 1{4046}$

031320
$\dfrac 3{392}$

031321
$(-6,\dfrac{19}{54})$

031322
$2$

031323
A

031324
B

031325
B

031326
D

031327
(1) $\arctan 35$; (2) $3\sqrt{2}$

031328
(1) $33.7$岁; (2) $\chi^2\approx 87.366>3.841$, 所以有骑行绿道与万元级运动自行车购买意愿有关

031329
(1) 约为$65.7\text{cm}^2$; (2) 参考改进建议: \textcircled{1} 雨伞不遮挡视线; \textcircled{2} 伞面为弧形，改进模型将伞设为一段圆弧; \textcircled{3} 考虑伞柄可以伸缩; \textcircled{4} 人体改进为立体模型; \textcircled{5} 考虑风速、风向; \textcircled{6} 考虑撑伞的省力、稳定等.

031330
(1) $\dfrac 12$; (2) 证明略; (3) $\dfrac 49x^2+\dfrac 45 y^2=1$($y>0$)

031331
(1) $a=-1$; (2) 当$a\ge 0$时, $f(x)$在$(0,+\infty)$上是严格增函数; 当$a<0$时, $f(x)$在$(0,-\dfrac 1a]$上是严格增函数, 在$[-\dfrac 1a,+\infty)$上是严格减函数; (3) (i) $(-\dfrac 1{\mathrm{e}},0)$; (ii) $(\dfrac 12,+\infty)$

014743
$\pi$

014744
$1$

014745
$9$

014746
$80$

014747
$3$

014748
$0.3$

014749
$\dfrac{\sqrt{3}}3\pi$

014750
$9$

014751
$8$

014752
$1$

014753
$[16-\sqrt{2},16+\sqrt{2}]$

014754
$10-4\sqrt{7}$

014755
D

014756
A

014757
B

014758
B

014759
(1) $\dfrac\pi 3$; (2) 最大值为$6$

014760
(1) $\dfrac 56$; (2) 证明略($H$和点$E$重合); (3) $\arcsin\dfrac{\sqrt{6}}3$

014761
(1) 证明略; $a_n=5^{n-1}+1$; (2) $999$

014762
(1) $\dfrac{x^2}4+\dfrac{y^2}3=1$; (2) $4$; (3) $8$

014763
(1) $0$是极大值点, $2$是极小值点; (2) $[\dfrac 72-\ln 4,+\infty)$; (3) 证明略