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录入第三轮复习讲义答案

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weiye.wang 2023-05-09 22:27:04 +08:00
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185
工具/文本文件/metadata.txt
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@ -1,15 +1,182 @@
ans
014613
$(-8,-7)$
014969
$2\sqrt{2}-3$
014615
$\dfrac{\sqrt{2}}2$
014970
$[-1,0]$
014961
$\dfrac 23\sqrt{3}$
014971
$11$
014953
$a=3$, $b=4$
014972
$\dfrac{\pi}{9}$
014962
014965
$(-\infty,8-4\sqrt{2}]$
040558
$[0,2-\ln 2]$
014966
D
014968
(1) 定值为$20$, 证明略; (2) $x=5$且$-5\le y\le 5$
014973
$\dfrac{2\sqrt{6}}3$
040556
(1) $[-\dfrac 43,0]$; (2) $50-6\sqrt{41}$; (3) $[2,5+3\sqrt{2}]$
040560
$(-\infty,\dfrac 12]$
040563
$(1,5)$
040564
$8$
040568
$\dfrac{29}{13}$
014884
$\{0\}\cup (1,3]$
014887
$(-\infty,-5]$
014894
B
014897
$(-\infty,-\dfrac 49)$
014891
(1) 证明略; (2) $f(x)=-\dfrac x{2+x}$; (3) $(\dfrac{1}{101},\dfrac{1}{99})$
014725
$2$或$\sqrt{6}$
014924
$36$
014926
B
014733
$(-\infty,-\dfrac{\sqrt{3a}}3]$和$[\dfrac{\sqrt{3a}}3,+\infty)$
014882
(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)
014931
$36$
014736
$(-\infty,-2]\cup [\dfrac 12,+\infty)$
014930
D
014922
$a=0$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
014925
证明略
014943
$(\dfrac 32,2)$
014909
(1) $[-1,6]$; (2) $[-13,9]$
031397
$\{\dfrac 12\}$
031398
证明略
031399
(1) 存在, 理由略; (2) 存在, 理由略; (3) 存在, 理由略
014944
$12\pi$
031400
$(-\infty,-6)\cup (6,+\infty)$
014989
\textcircled{2}\textcircled{3}
031401
$\sqrt{10}$
014910
(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
014987
$4\pi$
014913
(1) $d(P_1,l_1)=1$, $d(P_2,l_1)=\sqrt{5}$;\\
(2) $D=\left\{(x,y)|\begin{cases}x\ge 2, \\ (x-2)^2+(y-2)^2=1,\end{cases}\text{ 或 } \begin{cases} x\le =2, \\ (x+2)^2+(y-2)^2=1, \end{cases}\text{ 或 }\begin{cases} -2<x<2, \\ y=1 \text{或} 3\end{cases}\right\}$;\\
(3) $\Omega = \{(0,y)|y \in \mathbf{R}\}$
014990
(1) 证明略; (2) $[-\dfrac 14,+\infty)$
014914
(1) 是$T$点列, 理由略; (2) 是钝角三角形, 证明略; (3) 证明略
014911
$(2,3)$
014991
A
014992
C
014994
\textcircled{2}\textcircled{4}
014946
证明略
014995
(1) $2,5,8,11,8,5,2$;\\
(2) $k=13$时$S_{2k-1}$取到最大, 最大值为$626$;\\
(3) 共有四种满足要求的数列:\\
第一种: $1,2,\cdots,2^{m-2},2^{m-1},2^{m-1},2^{m-2},\cdots,2,1$($2m$项), $S_{2022}=\begin{cases}2^{m+1}-2^{2m-2022}-1, & 1500<m\le 2022,\\2^{2022}-1, & m \ge 2022;\end{cases}$\\
第二种: $1,2,\cdots,2^{m-2},2^{m-1},2^{m-2},\cdots,2,1$($2m-1$项), $S_{2022}=\begin{cases}3\cdot 2^{m+1}-2^{2m-2023}-1, & 1500<m\le 2022,\\2^{2022}-1, & m \ge 2022;\end{cases}$\\
第三种: $2^{m-1},2^{m-2},\cdots,2,1,1,2,\cdots,2^{m-2},2^{m-1}$($2m$项), $S_{2022}=\begin{cases}2^m+2^{2022-m}-2, & 1500<m\le 2022,\\2^m-2^{m-2022}, & m \ge 2022;\end{cases}$\\
第四种: $2^{m-1},2^{m-2},\cdots,2,1,2,\cdots,2^{m-2},2^{m-1}$($2m$项), $S_{2022}=\begin{cases}2^m+2^{2023-m}-3, & 1500<m\le 2022,\\2^m-2^{m-2022}, & m \ge 2022;\end{cases}$
014916
是奇函数, 证明略
014901
\textcircled{3}
014918
(1) 证明略; (2) 证明略
014919
(1) 不是有界数列, 理由略; (2) 不是有界数列, 理由略
014917
是周期函数, 证明略
014915
证明略
014905
(1) $a_n=n+5$, $b_n=3n+2$; (2) 存在, $m=11$
014907
(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$[-1,-\dfrac 12]\cup [\dfrac 52,5]$

114
题库0.3/Problems.json
View File

@ -384081,7 +384081,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$2$或$\\sqrt{6}$",
"solution": "",
"duration": -1,
"usages": [],
@ -384241,7 +384241,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "$(-\\infty,-\\dfrac{\\sqrt{3a}}3]$和$[\\dfrac{\\sqrt{3a}}3,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -384301,7 +384301,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,-2]\\cup [\\dfrac 12,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -388171,7 +388171,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(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)",
"solution": "",
"duration": -1,
"usages": [],
@ -388211,7 +388211,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\{0\\}\\cup (1,3]$",
"solution": "",
"duration": -1,
"usages": [],
@ -388271,7 +388271,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,-5]$",
"solution": "",
"duration": -1,
"usages": [],
@ -388351,7 +388351,7 @@
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"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) $f(x)=-\\dfrac x{2+x}$; (3) $(\\dfrac{1}{101},\\dfrac{1}{99})$",
"solution": "",
"duration": -1,
"usages": [],
@ -388411,7 +388411,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
@ -388471,7 +388471,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "$(-\\infty,-\\dfrac 49)$",
"solution": "",
"duration": -1,
"usages": [],
@ -388551,7 +388551,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "\\textcircled{3}",
"solution": "",
"duration": -1,
"usages": [],
@ -388631,7 +388631,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $a_n=n+5$, $b_n=3n+2$; (2) 存在, $m=11$",
"solution": "",
"duration": -1,
"usages": [],
@ -388671,7 +388671,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(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$[-1,-\\dfrac 12]\\cup [\\dfrac 52,5]$",
"solution": "",
"duration": -1,
"usages": [],
@ -388711,7 +388711,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "(1) $[-1,6]$; (2) $[-13,9]$",
"solution": "",
"duration": -1,
"usages": [],
@ -388731,7 +388731,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(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",
"solution": "",
"duration": -1,
"usages": [],
@ -388751,7 +388751,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(2,3)$",
"solution": "",
"duration": -1,
"usages": [],
@ -388793,7 +388793,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $d(P_1,l_1)=1$, $d(P_2,l_1)=\\sqrt{5}$;\\\\\n(2) $D=\\left\\{(x,y)|\\begin{cases}x\\ge 2, \\\\ (x-2)^2+(y-2)^2=1,\\end{cases}\\text{ 或 } \\begin{cases} x\\le =2, \\\\ (x+2)^2+(y-2)^2=1, \\end{cases}\\text{ 或 }\\begin{cases} -2<x<2, \\\\ y=1 \\text{或} 3\\end{cases}\\right\\}$;\\\\\n(3) $\\Omega = \\{(0,y)|y \\in \\mathbf{R}\\}$",
"solution": "",
"duration": -1,
"usages": [],
@ -388814,7 +388814,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 是$T$点列, 理由略; (2) 是钝角三角形, 证明略; (3) 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -388834,7 +388834,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -388854,7 +388854,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "是奇函数, 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -388874,7 +388874,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "是周期函数, 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -388894,7 +388894,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -388915,7 +388915,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 不是有界数列, 理由略; (2) 不是有界数列, 理由略",
"solution": "",
"duration": -1,
"usages": [],
@ -388975,7 +388975,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "$a=0$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",
"solution": "",
"duration": -1,
"usages": [],
@ -389015,7 +389015,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$36$",
"solution": "",
"duration": -1,
"usages": [],
@ -389035,7 +389035,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -389055,7 +389055,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
@ -389135,7 +389135,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -389155,7 +389155,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$36$",
"solution": "",
"duration": -1,
"usages": [],
@ -389411,7 +389411,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(\\dfrac 32,2)$",
"solution": "",
"duration": -1,
"usages": [],
@ -389431,7 +389431,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$12\\pi$",
"solution": "",
"duration": -1,
"usages": [],
@ -389471,7 +389471,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -389851,7 +389851,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,8-4\\sqrt{2}]$",
"solution": "",
"duration": -1,
"usages": [],
@ -389871,7 +389871,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -389911,7 +389911,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 定值为$20$, 证明略; (2) $x=5$且$-5\\le y\\le 5$",
"solution": "",
"duration": -1,
"usages": [],
@ -389931,7 +389931,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$2\\sqrt{2}-3$",
"solution": "",
"duration": -1,
"usages": [],
@ -389951,7 +389951,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$[-1,0]$",
"solution": "",
"duration": -1,
"usages": [],
@ -389972,7 +389972,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$11$",
"solution": "",
"duration": -1,
"usages": [],
@ -389992,7 +389992,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{\\pi}{9}$",
"solution": "",
"duration": -1,
"usages": [],
@ -390012,7 +390012,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "$\\dfrac{2\\sqrt{6}}3$",
"solution": "",
"duration": -1,
"usages": [],
@ -390292,7 +390292,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$4\\pi$",
"solution": "",
"duration": -1,
"usages": [],
@ -390332,7 +390332,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "\\textcircled{2}\\textcircled{3}",
"solution": "",
"duration": -1,
"usages": [],
@ -390352,7 +390352,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) $[-\\dfrac 14,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -390372,7 +390372,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "A",
"solution": "",
"duration": -1,
"usages": [],
@ -390392,7 +390392,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
@ -390434,7 +390434,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "\\textcircled{2}\\textcircled{4}",
"solution": "",
"duration": -1,
"usages": [],
@ -390454,7 +390454,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $2,5,8,11,8,5,2$;\\\\\n(2) $k=13$时$S_{2k-1}$取到最大, 最大值为$626$;\\\\\n(3) 共有四种满足要求的数列:\\\\\n第一种: $1,2,\\cdots,2^{m-2},2^{m-1},2^{m-1},2^{m-2},\\cdots,2,1$($2m$项), $S_{2022}=\\begin{cases}2^{m+1}-2^{2m-2022}-1, & 1500<m\\le 2022,\\\\2^{2022}-1, & m \\ge 2022;\\end{cases}$\\\\\n第二种: $1,2,\\cdots,2^{m-2},2^{m-1},2^{m-2},\\cdots,2,1$($2m-1$项), $S_{2022}=\\begin{cases}3\\cdot 2^{m+1}-2^{2m-2023}-1, & 1500<m\\le 2022,\\\\2^{2022}-1, & m \\ge 2022;\\end{cases}$\\\\\n第三种: $2^{m-1},2^{m-2},\\cdots,2,1,1,2,\\cdots,2^{m-2},2^{m-1}$($2m$项), $S_{2022}=\\begin{cases}2^m+2^{2022-m}-2, & 1500<m\\le 2022,\\\\2^m-2^{m-2022}, & m \\ge 2022;\\end{cases}$\\\\\n第四种: $2^{m-1},2^{m-2},\\cdots,2,1,2,\\cdots,2^{m-2},2^{m-1}$($2m$项), $S_{2022}=\\begin{cases}2^m+2^{2023-m}-3, & 1500<m\\le 2022,\\\\2^m-2^{m-2022}, & m \\ge 2022;\\end{cases}$",
"solution": "",
"duration": -1,
"usages": [],
@ -529906,7 +529906,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "$\\{\\dfrac 12\\}$",
"solution": "",
"duration": -1,
"usages": [],
@ -529929,7 +529929,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -529952,7 +529952,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 存在, 理由略; (2) 存在, 理由略; (3) 存在, 理由略",
"solution": "",
"duration": -1,
"usages": [],
@ -529977,7 +529977,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,-6)\\cup (6,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -530000,7 +530000,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\sqrt{10}$",
"solution": "",
"duration": -1,
"usages": [],
@ -542116,7 +542116,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "(1) $[-\\dfrac 43,0]$; (2) $50-6\\sqrt{41}$; (3) $[2,5+3\\sqrt{2}]$",
"solution": "",
"duration": -1,
"usages": [],
@ -542158,7 +542158,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$[0,2-\\ln 2]$",
"solution": "",
"duration": -1,
"usages": [],
@ -542198,7 +542198,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,\\dfrac 12]$",
"solution": "",
"duration": -1,
"usages": [],
@ -542258,7 +542258,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(1,5)$",
"solution": "",
"duration": -1,
"usages": [],
@ -542278,7 +542278,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$8$",
"solution": "",
"duration": -1,
"usages": [],
@ -542360,7 +542360,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{29}{13}$",
"solution": "",
"duration": -1,
"usages": [],