diff --git a/工具v4/文本文件/metadata.txt b/工具v4/文本文件/metadata.txt index 151bf466..c5c2ddb7 100644 --- a/工具v4/文本文件/metadata.txt +++ b/工具v4/文本文件/metadata.txt @@ -1,440 +1,171 @@ -ans +usages -010689 -证明略 -041040 -(1) $\overrightarrow{a}=(1,0,0)$.\\ -(2) $\overrightarrow{b}=(0,1,0)$.\\ -(3) $\overrightarrow{c}=(3 \sqrt{2}, 0,4)$.\\ -(4) $\overrightarrow{d}=(0,3 \sqrt{2}, 8)$. +004572 +20240619 2025届高二10班 0.967 -041041 -(1) 平面 $AA_1D_1D$.\\ -(2) 平面 $BB_1D_1D$. -010793 -(1)$\dfrac34$\\(2)变大 +004573 +20240619 2025届高二10班 0.967 -041042 -(1)$y=4x-2$\\(2)$[\dfrac{\pi}{4},\dfrac{\pi}{2})$ -022023 -(1)$(2,4)$\\(2)$(-\dfrac32,\dfrac94)$\\(3)$(\dfrac12,\dfrac14)$ +004574 +20240619 2025届高二10班 0.933 -022025 -$x=k\pi,k\in \mathbb{Z}$ -041043 -$\dfrac{\sqrt{2}}{2}$ +004575 +20240619 2025届高二10班 0.667 -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)$\ln{x}+1$ -022028 -(1)$y'=\dfrac{\cos x}{x}-\dfrac{\sin x}{x^2}$\\(2)$y'=\dfrac{2x}{\ln x}-\dfrac{x}{\ln^2{x}}$\\(3)$y'=\dfrac{1}{x\ln {10}}$ +004576 +20240619 2025届高二10班 0.900 -041047 -$1-\dfrac{\sqrt{2}}{2}$ -041048 -$-\dfrac13,\dfrac{13}{6}$ +004577 +20240619 2025届高二10班 0.917 -041049 -$\dfrac59,\dfrac{5}{36}$ -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$p=\dfrac13$ +004578 +20240619 2025届高二10班 0.700 -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 +004572 +20240619 2025届高二03班 1.000 -019245 -(1)$0.1\%$ -(2)$95.5\%$ -041153 -$\textcircled{3},\textcircled{4}$ +004573 +20240619 2025届高二03班 1.000 -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'' +004574 +20240619 2025届高二03班 0.976 -021270 -$(0,-8)$;$y=8$ -021271 -$(0,\frac{1}{16})$;$y=-\frac{1}{16}$ +004575 +20240619 2025届高二03班 0.793 -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$x^2=-12y$. +004576 +20240619 2025届高二03班 0.951 -021276 -$\frac{5}{2}$ -021279 -$(3,\pm 2\sqrt{3})$ +004577 +20240619 2025届高二03班 1.000 -021284 -$(3,\pm 2\sqrt{6})$ -021269 -A +004578 +20240619 2025届高二03班 0.866 -021275 -$(\frac{m}{4},0)$;$x=-\frac{m}{4}$ -041008 -$(0,\frac{1}{4a})$;$y=-\frac{1}{4a}$ +004572 +20240619 2025届高二04班 0.971 -041009 -$y^2=12x$ -041010 -2 +004573 +20240619 2025届高二04班 0.971 -041011 -$y^2=-8x$;$m=\pm 2\sqrt{6}$ -008929 -$x^2=-y,x\in [-1,1]$ +004574 +20240619 2025届高二04班 0.971 -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 -$(1,\pm 2)$ +004575 +20240619 2025届高二04班 0.571 -041013 -最小值为4, $M(\frac{1}{4},1)$ -041014 -$x^2=-12y$ +004576 +20240619 2025届高二04班 1.000 -021280 -$y^2=x$ -041015 -$y^2=8x$ +004577 +20240619 2025届高二04班 1.000 -021304 -$\frac{\pi}{2}$ -021308 -$\frac{11}{2}$ +004578 +20240619 2025届高二04班 0.657 -021287 -$\frac{45}{8}$ -009840 -$(\frac{1}{4},0)$;$x=-\frac{1}{4}$ +004572 +20240619 2025届高二05班 0.951 -021309 -2 -021290 -$(\frac{1}{2},1)$ +004573 +20240619 2025届高二05班 0.780 -021291 -$y^2=2x$或$y^2=6x$ -041016 -相切 +004574 +20240619 2025届高二05班 0.951 -021339 -$x^2-x+y^2=0(x\neq 0)$ -021289 -$4\sqrt{3}$ +004575 +20240619 2025届高二05班 0.585 -021293 -3 -021294 -$(4,2)$ +004576 +20240619 2025届高二05班 0.805 -021295 -$-4$ -021305 -$y^2=\pm 4x$ +004577 +20240619 2025届高二05班 1.000 -013106 -$[-1,1]$ -021292 -B +004578 +20240619 2025届高二05班 0.927 -008930 -$0$或$-\frac{1}{2}$ -008934 -$4x-y-15=0$ +004572 +20240619 2025届高二07班 1.000 -008922 -$y=\frac{1}{4},x>\frac{1}{16}$ -021299 -2 +004573 +20240619 2025届高二07班 0.930 -021300 -$2\sqrt{15}$ -021321 -(1) 定点$(2,0)$;(2) 4 +004574 +20240619 2025届高二07班 0.860 -041017 -(1) 6; (2) $\frac{1}{32}$ -041018 -8 +004575 +20240619 2025届高二07班 0.616 -021316 -$\frac{11}{4}$ -021326 -8 +004576 +20240619 2025届高二07班 0.860 -021319 -$y=\pm \frac{\sqrt{3}}{3}x+1$ -041019 -$\frac{2}{p}$ +004577 +20240619 2025届高二07班 1.000 -041020 -D -041021 -(1) $\frac{5p}{8}$; (2) $-2$;$-\frac{p}{y_0}$ +004578 +20240619 2025届高二07班 0.721 -021331 -D -041022 -C +004572 +20240619 2025届高二09班 0.914 -041023 -必要不充分 -021334 -$y=2x-3,x \leq 2$; $y=2x-3,x \in [1,2]$ +004573 +20240619 2025届高二09班 0.971 -021335 -$y=-2x^2+8x-4$ -021336 -$y^2=8x-16$ +004574 +20240619 2025届高二09班 0.886 -021337 -$x^2+y^2=1$ -021338 -$3x+y-4=0(x \neq 1)$ +004575 +20240619 2025届高二09班 0.729 -021340 -$(x-1)^2+(y-2)^2=\frac{1}{9}$ -021341 -$x+2y-5=0$ +004576 +20240619 2025届高二09班 0.914 -021342 -$x^2+y^2=4(x>0,y>0)$ -021343 -$(x-3)^2=10y-15$ +004577 +20240619 2025届高二09班 0.929 -041024 -C -008846 -0或$-\frac{1}{2}$ +004578 +20240619 2025届高二09班 0.629 -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$01$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