182 lines
3.3 KiB
Plaintext
182 lines
3.3 KiB
Plaintext
ans
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014969
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$2\sqrt{2}-3$
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014970
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$[-1,0]$
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014971
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$11$
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014972
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$\dfrac{\pi}{9}$
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014965
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$(-\infty,8-4\sqrt{2}]$
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040558
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$[0,2-\ln 2]$
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014966
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D
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014968
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(1) 定值为$20$, 证明略; (2) $x=5$且$-5\le y\le 5$
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014973
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$\dfrac{2\sqrt{6}}3$
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040556
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(1) $[-\dfrac 43,0]$; (2) $50-6\sqrt{41}$; (3) $[2,5+3\sqrt{2}]$
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040560
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$(-\infty,\dfrac 12]$
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040563
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$(1,5)$
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040564
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$8$
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040568
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$\dfrac{29}{13}$
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014884
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$\{0\}\cup (1,3]$
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014887
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$(-\infty,-5]$
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014894
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B
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014897
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$(-\infty,-\dfrac 49)$
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014891
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(1) 证明略; (2) $f(x)=-\dfrac x{2+x}$; (3) $(\dfrac{1}{101},\dfrac{1}{99})$
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014725
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$2$或$\sqrt{6}$
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014924
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$36$
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014926
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B
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014733
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$(-\infty,-\dfrac{\sqrt{3a}}3]$和$[\dfrac{\sqrt{3a}}3,+\infty)$
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014882
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(1) 定值为$r$, 证明略; (2) 当$a=1$时, 周期为$1$; 当$a\in (0,1)\cup (1,+\infty)$时, 周期为$2$; (3) $S_n=n$($r=0$时)或$S_n=\dfrac 34n^2+\dfrac 54n$($r=3$时)
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014931
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$36$
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014736
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$(-\infty,-2]\cup [\dfrac 12,+\infty)$
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014930
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D
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014922
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$a=0$时, $f(x)$是偶函数; $a=1$时, $f(x)$是奇函数; $a\ne 0$且$a\ne 1$时, $f(x)$既不是奇函数, 又不是偶函数
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014925
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证明略
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014943
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$(\dfrac 32,2)$
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014909
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(1) $[-1,6]$; (2) $[-13,9]$
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031397
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$\{\dfrac 12\}$
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031398
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证明略
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031399
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(1) 存在, 理由略; (2) 存在, 理由略; (3) 存在, 理由略
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014944
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$12\pi$
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031400
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$(-\infty,-6)\cup (6,+\infty)$
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014989
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\textcircled{2}\textcircled{3}
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031401
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$\sqrt{10}$
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014910
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(1) (i) $A$与$B$被直线$l$分割; (ii) $A$与$C$不被直线$l$分割; (2) 如$x+y=0$, 理由略; (3) 证明略
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014987
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$4\pi$
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014913
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(1) $d(P_1,l_1)=1$, $d(P_2,l_1)=\sqrt{5}$;\\
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(2) $D=\left\{(x,y)|\begin{cases}x\ge 2, \\ (x-2)^2+(y-2)^2=1,\end{cases}\text{ 或 } \begin{cases} x\le =2, \\ (x+2)^2+(y-2)^2=1, \end{cases}\text{ 或 }\begin{cases} -2<x<2, \\ y=1 \text{或} 3\end{cases}\right\}$;\\
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(3) $\Omega = \{(0,y)|y \in \mathbf{R}\}$
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014990
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(1) 证明略; (2) $[-\dfrac 14,+\infty)$
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014914
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(1) 是$T$点列, 理由略; (2) 是钝角三角形, 证明略; (3) 证明略
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014911
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$(2,3)$
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014991
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A
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014992
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C
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014994
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\textcircled{2}\textcircled{4}
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014946
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证明略
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014995
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(1) $2,5,8,11,8,5,2$;\\
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(2) $k=13$时$S_{2k-1}$取到最大, 最大值为$626$;\\
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(3) 共有四种满足要求的数列:\\
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第一种: $1,2,\cdots,2^{m-2},2^{m-1},2^{m-1},2^{m-2},\cdots,2,1$($2m$项), $S_{2022}=\begin{cases}2^{m+1}-2^{2m-2022}-1, & 1500<m\le 2022,\\2^{2022}-1, & m \ge 2022;\end{cases}$\\
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第二种: $1,2,\cdots,2^{m-2},2^{m-1},2^{m-2},\cdots,2,1$($2m-1$项), $S_{2022}=\begin{cases}3\cdot 2^{m+1}-2^{2m-2023}-1, & 1500<m\le 2022,\\2^{2022}-1, & m \ge 2022;\end{cases}$\\
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第三种: $2^{m-1},2^{m-2},\cdots,2,1,1,2,\cdots,2^{m-2},2^{m-1}$($2m$项), $S_{2022}=\begin{cases}2^m+2^{2022-m}-2, & 1500<m\le 2022,\\2^m-2^{m-2022}, & m \ge 2022;\end{cases}$\\
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第四种: $2^{m-1},2^{m-2},\cdots,2,1,2,\cdots,2^{m-2},2^{m-1}$($2m$项), $S_{2022}=\begin{cases}2^m+2^{2023-m}-3, & 1500<m\le 2022,\\2^m-2^{m-2022}, & m \ge 2022;\end{cases}$
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014916
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是奇函数, 证明略
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014901
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\textcircled{3}
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014918
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(1) 证明略; (2) 证明略
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014919
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(1) 不是有界数列, 理由略; (2) 不是有界数列, 理由略
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014917
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是周期函数, 证明略
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014915
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证明略
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014905
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(1) $a_n=n+5$, $b_n=3n+2$; (2) 存在, $m=11$
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014907
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(1) $f_1(x)$存在短距, 不存在长距, $f_2(x)$存在短距, 也存在长距; (2) 存在满足条件的实数$a$, $a$的范围为$[-1,-\dfrac 12]\cup [\dfrac 52,5]$ |