From 595825e4d68456b412f44810106cab8366372727 Mon Sep 17 00:00:00 2001
From: "weiye.wang" <kj_wangweiye@126.com>
Date: Wed, 19 Jun 2024 22:15:44 +0800
Subject: [PATCH] =?UTF-8?q?=E4=B8=80=E4=BA=9B=E9=AB=98=E4=BA=8C=E7=9A=84?=
 =?UTF-8?q?=E7=AD=94=E6=A1=88?=
MIME-Version: 1.0
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Content-Transfer-Encoding: 8bit

---
 工具v4/文本文件/metadata.txt | 455 ++++++++++++++++++++++++++++++++---
 1 file changed, 418 insertions(+), 37 deletions(-)

diff --git a/工具v4/文本文件/metadata.txt b/工具v4/文本文件/metadata.txt
index e397f1fc..151bf466 100644
--- a/工具v4/文本文件/metadata.txt
+++ b/工具v4/文本文件/metadata.txt
@@ -1,59 +1,440 @@
 ans
 
-025088
-$1$
+010689
+证明略
 
-025089
-$(0,0)$
+041040
+(1) $\overrightarrow{a}=(1,0,0)$.\\
+(2) $\overrightarrow{b}=(0,1,0)$.\\
+(3) $\overrightarrow{c}=(3 \sqrt{2}, 0,4)$.\\
+(4) $\overrightarrow{d}=(0,3 \sqrt{2}, 8)$.
 
-025090
-$m$
+041041
+(1) 平面 $AA_1D_1D$.\\
+(2) 平面 $BB_1D_1D$.
 
-025091
-$5$
+010793
+(1)$\dfrac34$\\(2)变大
 
-025092
-$2x$
+041042
+(1)$y=4x-2$\\(2)$[\dfrac{\pi}{4},\dfrac{\pi}{2})$
 
-025093
-$\mathrm{i}$
+022023
+(1)$(2,4)$\\(2)$(-\dfrac32,\dfrac94)$\\(3)$(\dfrac12,\dfrac14)$
 
-025094
-$-\dfrac{3}{4}$
+022025
+$x=k\pi,k\in \mathbb{Z}$
 
-025095
-$\dfrac{1}{2}\pm \dfrac{\sqrt{3}}{2}\mathrm{i}$
+041043
+$\dfrac{\sqrt{2}}{2}$
 
-025096
-$[-1,3]$
+022027
+(1)$y'=\dfrac12x^{-\dfrac12}-\dfrac{1}{x}$\\(2)$3x^2-2x+1$\\(3)$\mathrm{e}^x(2x+x^2)$\\(4)$\dfrac12x^{-\dfrac12}\sin{x}+\sqrt{x}\cos{x}$\\(5)$\ln{x}+1$
 
-025097
-$\dfrac{1}{2}$
+022028
+(1)$y'=\dfrac{\cos x}{x}-\dfrac{\sin x}{x^2}$\\(2)$y'=\dfrac{2x}{\ln x}-\dfrac{x}{\ln^2{x}}$\\(3)$y'=\dfrac{1}{x\ln {10}}$
 
-025098
-$(0,\dfrac{\pi}{2})$
+041047
+$1-\dfrac{\sqrt{2}}{2}$
 
-025099
-A
+041048
+$-\dfrac13,\dfrac{13}{6}$
 
-025100
-A
+041049
+$\dfrac59,\dfrac{5}{36}$
 
-025101
+004609
+(1)$\dfrac{25}{32}$\\
+(2)分布列为$\begin{pmatrix}900 & 1500\\ -3p^3+6p^2-3p+1 & 3p^3-6p^2+3p\end{pmatrix}$, $E[X]$的最大值为$350$万元, 此时$p=\dfrac13$
+
+004610
+(1)$\dfrac{135}{512}$\\(2)分布列为$\begin{pmatrix}0 & 1 & 2 & \dots & n-1 & n\\ \dfrac14 & \dfrac34 \cdot \dfrac14 &  (\dfrac34)^2 \cdot \dfrac14 & \dots & (\dfrac34)^{n-1} \cdot \dfrac14 & (\dfrac34)^n\end{pmatrix}$,$E[X]=3-3(\dfrac34)^n$
+
+019240
 D
 
-025102
-(1) $6$; (2) $\pm 6$或$\pm 2\sqrt{11}$
+019245
+(1)$0.1\%$
+(2)$95.5\%$
 
-025103
-(1) $5$; (2) $\dfrac{-3\pm \sqrt{5}}{2}$
+041153
+$\textcircled{3},\textcircled{4}$
 
-025104
-(1) $2\sqrt{6}$; (2) $(\dfrac{\pi}{6},\dfrac{\pi}{4})$
+041206
+(1)$\frac{e}{2}$;(2) 任意 $a>0$,  $b>0$
+ 能使函数 $f(x)$ 与 $g(x)$ 在区间 $(0,+\infty)$ 内存在``$\mathrm{S}$ 点''
 
-025105
-(1) $a=-\dfrac{\pi}{6}$, $b=0$, $f(x)=2\sin (2x+\dfrac{\pi}{3})$, 最小正周期为$\pi$, 对称轴为$x=\dfrac{k\pi}{2}+\dfrac{\pi}{12}$, $k\in \mathbf{Z}$; (2) $[1,2)$; (3) $\dfrac{5\pi}{12}$
 
-032895
-(1) \textcircled{1}是``含谷函数'', 谷点是$0$, \textcircled{2} 不是含谷函数, 理由略; (2) $(2,18)$; (3) $\sqrt{2}$
+021270
+$(0,-8)$;$y=8$
 
+021271
+$(0,\frac{1}{16})$;$y=-\frac{1}{16}$
+
+021272
+$(0,-\frac{1}{6})$;$y=\frac{1}{6}$
+
+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$x^2=-12y$.
+
+021276
+$\frac{5}{2}$
+
+021279
+$(3,\pm 2\sqrt{3})$
+
+021284
+$(3,\pm 2\sqrt{6})$
+
+021269
+A
+
+021275
+$(\frac{m}{4},0)$;$x=-\frac{m}{4}$
+
+041008
+$(0,\frac{1}{4a})$;$y=-\frac{1}{4a}$
+
+041009
+$y^2=12x$
+
+041010
+2
+
+041011
+$y^2=-8x$;$m=\pm 2\sqrt{6}$
+
+008929
+$x^2=-y,x\in [-1,1]$
+
+041012
+(1) $(-1,0)$;$x=1$; (2) $\frac{x^2}{2}+y^2$=1; (3) $(4-3\sqrt{2},\pm \sqrt{12\sqrt{2}-16})$
+
+021278
+$(1,\pm 2)$
+
+041013
+最小值为4, $M(\frac{1}{4},1)$
+
+041014
+$x^2=-12y$
+
+021280
+$y^2=x$
+
+041015
+$y^2=8x$
+
+021304
+$\frac{\pi}{2}$
+
+021308
+$\frac{11}{2}$
+
+021287
+$\frac{45}{8}$
+
+009840
+$(\frac{1}{4},0)$;$x=-\frac{1}{4}$
+
+021309
+2
+
+021290
+$(\frac{1}{2},1)$
+
+021291
+$y^2=2x$或$y^2=6x$
+
+041016
+相切
+
+021339
+$x^2-x+y^2=0(x\neq 0)$
+
+021289
+$4\sqrt{3}$
+
+021293
+3
+
+021294
+$(4,2)$
+
+021295
+$-4$
+
+021305
+$y^2=\pm 4x$
+
+013106
+$[-1,1]$
+
+021292
+B
+
+008930
+$0$或$-\frac{1}{2}$
+
+008934
+$4x-y-15=0$
+
+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
+
+022029
+$\frac{2}{3}$
+
+022030
+(1)$y^{'}=20(5x-3)^{3}$;(2)$y^{'}=15(3x+2)^{4}$
+
+022031
+(1)$y^{'}=12(1-3x)^{-5}$;(2)$y^{'}=-\frac{3}{4}(3x+1)^{-\frac{5}{4}}$
+
+022032
+(1)$y^{'}=3\cos (3 x-\dfrac{\pi}{6})$;(2)$y^{'}=-2\sin{2x}$
+
+022033
+(1)$y=-x+\frac{\pi}{3}+\frac{\sqrt{3}}{2}$;(2)$y=(-6ln2)x+2$
+
+022034
+(1)$y^{'}=\mathrm{e}^{2x}(2\sin{3x}+3\cos{3x})$;(2)$y^{'}=\frac{1}{1-x^2}$;(3)$y^{'}=\frac{-2x^2+2x}{(2x+1)^4}$
+
+022035
+(1)在$\mathbf{R}$上严格递增;(2)在$(-\infty,0),(0,+\infty)$严格递增
+
+022036
+(1)在$(-\infty,1],[1,+\infty)$上严格递增, 在$[-1,0),(0,1]$上严格递减;(2)在$(-\infty,1]$上严减,在$[1,+\infty)$上严增;(3)在$(0,\frac{1}{e}]$上严减, 在$[\frac{1}{e},+\infty)$上严增
+
+022037
+在$(-\infty,1],[4,+\infty)$上严格递增,在$[2,4]$上严减
+
+022038
+(1)$(-\infty,0]$;(2)$[3,+\infty)$;(3)$a=3$;(4)$(0,3)$
+
+022039
+(1)在$(0,+\infty)$上严格减; (2)在$(0,\frac{\pi}{4})$上严格减
+
+022040
+略
+
+022041
+$1$
+
+022042
+在$(-\pi,\frac{\pi}{6}],[\frac{5\pi}{6},\pi)$上严增,在$[\frac{\pi}{6},\frac{5\pi}{6}]$上严格减,极大值为$f(\frac{\pi}{6})=\frac{\pi}{12}+\frac{\sqrt{3}}{2}$,极小值为$f(\frac{5\pi}{6})=\frac{5\pi}{12}-\frac{\sqrt{3}}{2}$
+
+022043
+$a=-3,b=-24$
+
+015852
+$(-\infty,-3)\cup(6,+\infty)$
+
+022044
+$\frac{1}{\mathrm{e}}$
+
+022045
+$(-\infty,-3]$
+
+041044
+$1-e$
+
+022046
+$f_{\max}(x)=f(-1)=10$, $f_{\min}(x)=f(-4)=-71$
+
+022047
+$f_{\max}(x)=f(\dfrac{\pi}{6})=\dfrac{\pi}{6}+\sqrt{3}$
+
+041045
+$e^{2}$
+
+041046
+(1)$h(t)=-t^3+t-1$;(2)$(1,+\infty)$
+
+031805
+(1)$S_{ABCD}=800\cos{\theta}(1+4\sin{\theta})$, $S_{\triangle CDP}=1600\cos{\theta}(1-\sin{\theta}),\sin{\theta}\in[\frac{1}{4},1)$;(2)当$\theta$为$\frac{\pi}{6}$时, 能使年总产值最大,最大值为$6000\sqrt{3}$
\ No newline at end of file