183 lines
2.6 KiB
Plaintext
183 lines
2.6 KiB
Plaintext
ans
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004353
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$[1,2)$
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004270
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$(-3,1]$
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004254
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$3$
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004145
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$1$
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004083
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$3$
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004232
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$\dfrac{34}{35}$
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004216
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$4$
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004149
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$[-\dfrac 12,1]$
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004172
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$\dfrac 12$
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004089
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$-1$与$\dfrac 12$
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004415
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$1$
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004135
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D
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004136
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C
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031282
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A
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004159
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(1) $2$; (2) $\arctan\dfrac{\sqrt{2}}4$
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004442
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(1) $\dfrac{\pi}{12}$或$\dfrac\pi 4$; (2) $\omega = \dfrac 23$, 单调递增区间为$[0,\dfrac\pi 2]$
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004721
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(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$16\sqrt{2}-16$
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004246
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(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$(6,24)$
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004352
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(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
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031311
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$\{4,5\}$
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031312
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$(1,11)$
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031313
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$-\dfrac 35+\dfrac 45\mathrm{i}$
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031314
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$1$
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031315
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$2\sqrt{3}$
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031316
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$2$
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031317
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$(-\dfrac 15,\dfrac 25)$
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031318
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$(1,5)$
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031319
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$\dfrac 1{4046}$
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031320
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$\dfrac 3{392}$
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031321
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$(-6,\dfrac{19}{54})$
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031322
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$2$
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031323
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A
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031324
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B
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031325
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B
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031326
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D
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031327
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(1) $\arctan 35$; (2) $3\sqrt{2}$
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031328
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(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
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031329
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(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.
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031330
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(1) $\dfrac 12$; (2) 证明略; (3) $\dfrac 49x^2+\dfrac 45 y^2=1$($y>0$)
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031331
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(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) $(\dfrac 12,+\infty)$
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014743
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$\pi$
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014744
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$1$
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014745
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$9$
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014746
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$80$
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014747
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$3$
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014748
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$0.3$
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014749
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$\dfrac{\sqrt{3}}3\pi$
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014750
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$9$
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014751
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$8$
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014752
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$1$
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014753
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$[16-\sqrt{2},16+\sqrt{2}]$
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014754
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$10-4\sqrt{7}$
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014755
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D
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014756
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A
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014757
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B
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014758
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B
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014759
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(1) $\dfrac\pi 3$; (2) 最大值为$6$
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014760
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(1) $\dfrac 56$; (2) 证明略($H$和点$E$重合); (3) $\arcsin\dfrac{\sqrt{6}}3$
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014761
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(1) 证明略; $a_n=5^{n-1}+1$; (2) $999$
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014762
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(1) $\dfrac{x^2}4+\dfrac{y^2}3=1$; (2) $4$; (3) $8$
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014763
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(1) $0$是极大值点, $2$是极小值点; (2) $[\dfrac 72-\ln 4,+\infty)$; (3) 证明略 |