From 93a6c1fc970db06bf7a0c026df29c9067e327194 Mon Sep 17 00:00:00 2001
From: wangweiye7840 <kj_wangweiye@126.com>
Date: Tue, 4 Jun 2024 11:39:14 +0800
Subject: [PATCH] =?UTF-8?q?25=E5=B1=8A=E4=B8=80=E4=BA=9B=E7=AD=94=E6=A1=88?=
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---
 工具v4/文本文件/metadata.txt | 574 ++++++++++++++++++++++++++++++-----
 1 file changed, 495 insertions(+), 79 deletions(-)

diff --git a/工具v4/文本文件/metadata.txt b/工具v4/文本文件/metadata.txt
index 0f84a3bd..89be7a75 100644
--- a/工具v4/文本文件/metadata.txt
+++ b/工具v4/文本文件/metadata.txt
@@ -1,122 +1,538 @@
 ans
 
-023644
-证明略
+021268
+\begin{center}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline 标准方程 & 图形 & 顶点 & 对称轴 & 焦点 & 准线 \\
+\hline $y^2=2 p x$($p>0$) & \begin{tikzpicture}[>=latex,scale = 0.5]
+\draw [->] (-2,0) -- (2,0) node [below] {$x$};
+\draw [->] (0,-2) -- (0,2) node [right] {$y$};
+\draw (0,0) node [below right] {$O$};
+\draw (-0.5,-2) -- (-0.5,2);
+\draw [domain = -2:2] plot ({\x*\x/2},\x);
+\end{tikzpicture} & $(0,0)$ & $x$轴 & $(\frac{p}{2},0)$ & $x=-\frac{p}{2}$ \\
+\hline $y^2=-2 p x$($p>0$)& \begin{tikzpicture}[>=latex,scale = 0.5]
+\draw [->] (-2,0) -- (2,0) node [below] {$x$};
+\draw [->] (0,-2) -- (0,2) node [right] {$y$};
+\draw (0,0) node [below right] {$O$};
+\draw (0.5,-2) -- (0.5,2);
+\draw [domain = -2:2] plot ({-\x*\x/2},\x);
+\end{tikzpicture} & $(0,0)$ & $x$轴 & $(-\frac{p}{2},0)$ & $x=\frac{p}{2}$ \\
+\hline $x^2=2 p y$($p>0$)& \begin{tikzpicture}[>=latex,scale = 0.5]
+\draw [->] (-2,0) -- (2,0) node [below] {$x$};
+\draw [->] (0,-2) -- (0,2) node [right] {$y$};
+\draw (0,0) node [below right] {$O$};
+\draw (-2,-0.5) -- (2,-0.5);
+\draw [domain = -2:2] plot (\x,{\x*\x/2});
+\end{tikzpicture}& $(0,0)$ & $y$轴 & $(0,\frac{p}{2})$ & $y=-\frac{p}{2}$ \\
+\hline $x^2=-2 p y$($p>0$)&\begin{tikzpicture}[>=latex,scale = 0.5]
+\draw [->] (-2,0) -- (2,0) node [below] {$x$};
+\draw [->] (0,-2) -- (0,2) node [right] {$y$};
+\draw (0,0) node [below right] {$O$};
+\draw (-2,0.5) -- (2,0.5);
+\draw [domain = -2:2] plot (\x,-{\x*\x/2});
+\end{tikzpicture} & $(0,0)$ & $y$轴 & $(0,-\frac{p}{2})$ & $y=\frac{p}{2}$ \\
+\hline
+\end{tabular}
+\end{center}
 
-019070
-(1) $f'(x)=2x\sin x+x^2 \cos x$; (2) $f'(x)=\dfrac{x^2+4x}{(x+2)^2}$; (3) $f'(x)=2x-4$
+021270
+$(0,-8)$; $y=8$
 
-019071
-证明略
+021271
+$(0,\frac{1}{16})$; $y=-\frac{1}{16}$
 
-019073
-$-4$或$\dfrac{1}{4}$
+021272
+$(0,-\frac{1}{6})$; $y=\frac{1}{6}$
 
-019074
-$-1$
+041007
+(1) $y^2=-x$; (2) $y^2=4x$或$y^2=-4x$或$x^2=-4y$或$x^2=4y$; (3)  $y^2=-\frac{16}{3}x$或 $x^2=\frac{9}{4}y$;
+(4) $y^2=16x$或$y^2=-16x$;
+(5) $y^2=16x$或$x^2=-12y$.
 
-009913
-(1) $3\mathrm{e}^x-\mathrm{e}x^{\mathrm{e}-1}$; (2) $-\sin x+\dfrac{2}{x^2}$; (3) $24x^2+24x+6$; (4) $\dfrac{1}{2}x^{-\frac{1}{2}}\sin x+\sqrt{x} \cos x$; (5) $\ln x+1+2x^{-3}$; (6) $1+\dfrac{1}{x^2}$; (7) $\dfrac{4x}{(x^2+1)^2}$; (8) $\dfrac{1}{\cos^2 x}$
+021276
+$\frac{5}{2}$
 
-019076
-证明略
+021279
+$(3,\pm 2\sqrt{3})$
 
-000143
-(1) $\sqrt{58}$; (2) $k=-\dfrac{1}{3}$, 反向
+021284
+$(3,\pm 2\sqrt{6})$
 
-000144
-(1) $\overrightarrow{AB}=(-9,15)$, $|\overrightarrow{AB}|=3\sqrt{34}$; (2) $\overrightarrow{OC}=(3,6)$, $\overrightarrow{OD}=(19,-39)$; (3) $-56$
+021269
+A
 
-000146
-$\lambda=1$, $\mu=-2$
+021275
+$(\frac{m}{4},0)$;$x=-\frac{m}{4}$
 
-000148
-$(\dfrac{1}{3},-\dfrac{5}{3})$
+041008
+$(0,\frac{1}{4a})$;$y=-\frac{1}{4a}$
 
-000149
-证明略
+041009
+$y^2=12x$
 
-000152
-(1) 证明略; (2) $\dfrac{\pi}{6}$或$\dfrac{7\pi}{6}$
+041010
+2
 
-000155
-$k=-\dfrac{2}{3}$
+041011
+$y^2=-8x$;$m=\pm 2\sqrt{6}$
 
-000157
-证明略
+008929
+$x^2=-y,x\in [-1,1]$
 
-000160
-不存在
+041012
+(1) $(-1,0)$;$x=1$; (2) $\frac{x^2}{2}+y^2$=1; (3) $(4-3\sqrt{2},\pm \sqrt{12\sqrt{2}-16})$
 
-024842
-$1$
+021278
+$(1,\pm 2)$
 
-014777
-$\mathrm{e}$
+041013
+最小值为$4$, $M(\frac{1}{4},1)$
 
-024843
-$2x\cos x-x^2 \sin x$
+041014
+$x^2=-12y$
 
-024844
-$(1,-8)$或$(-1,-12)$
+021280
+$y^2=x$
 
-024845
-$y=2\sqrt{2}x-1$或$y=-2\sqrt{2} x-1$
+041015
+$y^2=8x$
 
-024846
-$1+\sqrt{2}$
+021304
+$\frac{\pi}{2}$
 
-024847
-$3$或$-1$
+021308
+$\frac{11}{2}$
 
-024849
-$-\dfrac{8}{15}{}^\circ/\mathrm{min}$
+021287
+$\frac{45}{8}$
 
-041168
-$-6-3\Delta t$
+009840
+$(\frac{1}{4},0)$;$x=-\frac{1}{4}$
 
-041170
-\textcircled{3}
+021309
+2
 
-041171
-等于
+021290
+$(\frac{1}{2},1)$
 
-041173
-$2$
+021291
+$y^2=2x$或$y^2=6x$
 
-041174
-$-\dfrac{1}{2}$
+041016
+相切
 
-041175
-$\dfrac{1}{3}\text{m/s}$
+021339
+$x^2-x+y^2=0(x\neq 0)$
 
-041176
-$-2$
+021289
+$4\sqrt{3}$
 
-023654
-$\dfrac{10}{3}$
+021293
+3
 
-041191
-$3$
+021294
+$(4,2)$
 
-041192
+021295
 $-4$
 
-041193
-$y=x+1$与$y=-3x-3$
+021305
+$y^2=\pm 4x$
 
-041194
-$\dfrac{3}{4}$
+013106
+$[-1,1]$
 
-041177
-$\sqrt{2}$
+021292
+B
 
-041178
-(1) $y=-2x+1$; (2) $y=x-\dfrac{1}{4}$
+008930
+$0$或$-\frac{1}{2}$
 
-024850
-(1) $f'(x)=\mathrm{e}^x-\cos x$; (2) $f'(x)=-\dfrac{1}{x\ln 3}$; (3) $f'(x)=2\sin x\cos x$; (4) $f'(x)=\dfrac{1}{\cos^2 x}$; (5) $f'(x)=-\dfrac{\cos x}{\sin^2 x}$; (6) $f'(x)=\dfrac{1}{2}x^{-\frac{1}{2}}-x^{-2}$; (7) $f'(x)=3x^2+6x+3$; (8) $f'(x)=\dfrac{1}{x}$
+008934
+$4x-y-15=0$
 
-041197
-(1) $y'=\dfrac{\sin x-\cos x-1}{(1+\cos x)^2}$; (2) $y'=3x^2-\dfrac{3}{x}x^{-\frac{5}{2}}+\dfrac{\cos x}{x^2}-\dfrac{2\in x}{x^3}$; (3) $y'=\dfrac{4}{(1-x)^2}$; (4) $y'=\tan x+\dfrac{x}{\cos^2 x}$
+008922
+$y=\frac{1}{4},x>\frac{1}{16}$
 
+021299
+2
+
+021300
+$2\sqrt{15}$
+
+021321
+(1) 定点$(2,0)$;(2) 4
+
+041017
+(1) 6; (2) $\frac{1}{32}$
+
+041018
+8
+
+021316
+$\frac{11}{4}$
+
+021326
+8
+
+021319
+$y=\pm \frac{\sqrt{3}}{3}x+1$
+
+041019
+$\frac{2}{p}$
+
+041020
+D
+
+041021
+(1) $\frac{5p}{8}$; (2) $-2$;$-\frac{p}{y_0}$
+
+021331
+D
+
+041022
+C
+
+041023
+必要不充分
+
+021334
+$y=2x-3,x \leq 2$; $y=2x-3,x \in [1,2]$
+
+021335
+$y=-2x^2+8x-4$
+
+021336
+$y^2=8x-16$
+
+021337
+$x^2+y^2=1$
+
+021338
+$3x+y-4=0(x \neq 1)$
+
+021340
+$(x-1)^2+(y-2)^2=\frac{1}{9}$
+
+021341
+$x+2y-5=0$
+
+021342
+$x^2+y^2=4(x>0,y>0)$
+
+021343
+$(x-3)^2=10y-15$
+
+041024
+C
+
+008846
+0或$-\frac{1}{2}$
+
+008847
+$\frac{3}{2}$
+
+008852
+0或$\frac{1}{4}$或$-\frac{1}{2}$
+
+008853
+$[-4,4]]$
+
+041025
+(2) $13x-2y=0$
+
+041026
+$(-3,5),(1,1)$
+
+041027
+$k<-2$或$k>2$或$k=\pm \sqrt{3}$
+
+010704
+$(-\frac{2\sqrt{13}}{13},\frac{2\sqrt{13}}{13})$
+
+010703
+当$0<k<1$时,轨迹为椭圆;当$k>1$时,轨迹为双曲线;当$k=1$时,轨迹为抛物线
+
+021348
+$x^2+4(y-1)^2=4(0 \leq x \leq 2, 1 \leq y \leq 2)$
+
+021349
+0
+
+021351
+$\frac{\pi}{3}$或$\frac{2\pi}{3}$
+
+041028
+$(\frac{3\sqrt{3}}{2},1)$; $\arctan \frac{2\sqrt{3}}{9}$
+
+021352
+4
+
+021353
+D
+
+041029
+$x=a+r\cos \alpha, y=b+r \sin \alpha$ ($\alpha$为参数, $\alpha \in \mathbf{R}$)
+
+021354
+(1) $M_1$在曲线$C$上, $M_2$不在曲线$C$上; (2) $a=9$
+
+021355
+$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$双曲线
+
+009845
+$x=\frac{2+\cos \alpha}{2}, y=\frac{\sin  \alpha}{2}$ ($\alpha$为参数, $\alpha \in \mathbf{R}$)
+
+009846
+$x=1+9t,y=1+12t$,其中 $t$ 为参数,$t\geq 0$
+
+021358
+6
+
+021359
+$\sqrt{17}$
+
+021362
+$(3\sqrt{2},\sqrt{2})$
+
+021363
+最大值7; 最小值$\frac{3\sqrt{15}-4}{4}$
+
+021364
+$\sqrt{33}+2\sqrt{6}$
+
+012470
+B
+
+041030
+B
+
+041031
+A
+
+041032
+$(-3,-\frac{3\sqrt{5}}{5}) \cup (\frac{3\sqrt{5}}{5},3)$
+
+041033
+13
+
+041034
+$\frac{1+2\sqrt{21}}{3}$
+
+041035
+$y=\pm  1$
+
+041036
+$y^2=2x-2$
+
+041037
+$7\sqrt{3}$
+
+041038
+(1) $C_1$是以$(-4,3)$为圆心,半径为1的圆; $C_2$是椭圆 
+$\frac{x^2}{64}+\frac{y^2}{9}=1$; (2) $\frac{8\sqrt{5}}{5}$
+
+041039
+(1) $x=1$,$5x-2y-3=0$,$2x-y-1=0$,$2x+y-3=0$;
+(2) 点 $T$ 不在曲线 $\Gamma$ 上
+
+ans
+
+041073
+(-2,$\dfrac{1}{2}$)
+
+041074
+$x-8y=0(x<-\dfrac{8}{15}\sqrt{15}$或$x>\dfrac{8}{15}\sqrt{15}$)
+
+041075
+$(-\infty,-1)\cup(1,+\infty)$
+
+041076
+$[3+2\sqrt{3},+\infty)$
+
+041077
+$2\sqrt{10}$
+
+041078
+44
+
+002112
+$y^2=4x$
+
+002409
+$y^2=-\dfrac{9}{2}x$或$x^2=\dfrac{4}{3}y$
+
+041079
+$\pm 2\sqrt{6}$
+
+041080
+(5,0)
+
+041081
+$\dfrac{23}{24}$
+
+041082
+176.0
+
+041083
+$|PA|_{\min}=\begin{cases}
+    a,0<a\leq1\\
+    \sqrt{2a-1},a>1
+\end{cases}$
+
+041084
+不存在
+
+041085
+(1)$m_A=91.5,m_B=90\\(2)S^2_A<S^2_B,A$稳定\\(3)$\dfrac{4}{5}$
+
+041086
+(1)$1<a<\sqrt{10}\\(2)l:x=3$或$x=\pm \dfrac{5}{7}\sqrt{7}+3$
+
+041087
+(1)$d=2$\\(2)$P$不存在\\(3)$l:x=\pm \sqrt{2}y+2$
+
+002112
+$y^2=4x$
+
+002409
+$y^2=-\dfrac{9}{2}x$或$x^2=\dfrac{4}{3}y$
+
+041079
+$\pm 2\sqrt{6}$
+
+041080
+$(5,0)$
+
+041088
+$2x\pm \sqrt{3}y-2=0$
+
+003441
+$\dfrac{11}{4}$
+
+041089
+$2x+y-2=0$
+
+041090
+$(2,2)$
+
+041091
+1$\quad(\dfrac{1}{9},\dfrac{2}{3})$
+
+041092
+$48$
+
+041093
+C
+
+041094
+$S_{max}=30$此时$P(8,4)$
+
+041095
+(1)$x_B+x_C=11\\y_B+y_C=-4$\\(2)$BC:y=-4x+20$\\(3)$B(\dfrac{11-\sqrt{21}}{2},-2+2\sqrt{21})$\\C($\dfrac{11+\sqrt{21}}{2},-2-2\sqrt{21})$
+
+041096
+$(1)C_2:\dfrac{y^2}{4}-\dfrac{x^2}{3}=1\\(2)p>\dfrac{4}{3}\sqrt{3},\quad \overrightarrow{FA}\cdot \overrightarrow{FB}_{max}=9,\quad$此时$p=2\sqrt{3}$\\(3)$p=2\sqrt{3}$
+
+041097
+$(-\infty,-2)$
+
+041098
+$\dfrac{1}{2}$
+
+041099
+(2)(3)(4)
+
+018928
+7
+
+041100
+AD,CD
+
+041101
+(3)(4)
+
+041102
+$\pm 2$
+
+041103
+$y^2-\dfrac{x^2}{48}=1\quad(y<0)$
+
+041104
+4或2或$\dfrac{3}{2}$
+
+041105
+(2)
+
+023553
+(1)$\dfrac{17}{45}$\\(2)一级6箱，二级2箱\\(3)预估287.69克
+
+041106
+$[\dfrac{1}{3},1)\cup(1,3]$
+
+018949
+没有被抓的风险
+
+041107
+(1)$\dfrac{x^2}{24}+\dfrac{y^2}{20}=1\\S_{max}=\dfrac{5\sqrt{30}}{4}$
+
+041108
+D
+
+041109
+C
+
+041110
+A
+
+041111
+B
+
+041112
+$\dfrac{2}{5}\sqrt{10}$
+
+041113
+A
+
+030201
+B
+
+041114
+A
+
+041115
+$(\sqrt{3},2)$
+
+041116
+$\dfrac{\sqrt{2}}{2}$
+
+041117
+(1)$arccos\dfrac{2}{5}\\$(2)正弦值为$\dfrac{\sqrt{15}}{5}\\(3)\dfrac{\pi}{6}$
+
+041118
+$l:y-2=\dfrac{118}{143}(x-3)$
+
+041119
+$x^2+y^2+x-6y+3=0$
+
+041120
+曲线方程为$y^2=48-12x\quad(x\geq3)$及$y^2=4x\quad(x<3)$
+
+041121
+$x^2+y^2=7$
+
+
+ans
+
+012345
+D
+
+023233
+$a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
+    \end{cases}$.
+
+023255
+(1)略；(2)$a_n=\begin{cases}
+    \frac{1}{2},n=1\\-\frac{1}{2n(n-1)},n\geq2
+\end{cases}$