使用记录0619

工具v4/文本文件/metadata.txt

@@ -1,440 +1,171 @@
-ans
+usages
 
-010689
-证明略
 
-041040
+004572
-(1) $\overrightarrow{a}=(1,0,0)$.\\
+20240619	2025届高二10班	0.967
-(2) $\overrightarrow{b}=(0,1,0)$.\\
-(3) $\overrightarrow{c}=(3 \sqrt{2}, 0,4)$.\\
-(4) $\overrightarrow{d}=(0,3 \sqrt{2}, 8)$.
 
-041041
-(1) 平面 $AA_1D_1D$.\\
-(2) 平面 $BB_1D_1D$.
 
-010793
+004573
-(1)$\dfrac34$\\(2)变大
+20240619	2025届高二10班	0.967
 
-041042
-(1)$y=4x-2$\\(2)$[\dfrac{\pi}{4},\dfrac{\pi}{2})$
 
-022023
+004574
-(1)$(2,4)$\\(2)$(-\dfrac32,\dfrac94)$\\(3)$(\dfrac12,\dfrac14)$
+20240619	2025届高二10班	0.933
 
-022025
-$x=k\pi,k\in \mathbb{Z}$
 
-041043
+004575
-$\dfrac{\sqrt{2}}{2}$
+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
+004576
-(1)$y'=\dfrac{\cos x}{x}-\dfrac{\sin x}{x^2}$\\(2)$y'=\dfrac{2x}{\ln x}-\dfrac{x}{\ln^2{x}}$\\(3)$y'=\dfrac{1}{x\ln {10}}$
+20240619	2025届高二10班	0.900
 
-041047
-$1-\dfrac{\sqrt{2}}{2}$
 
-041048
+004577
-$-\dfrac13,\dfrac{13}{6}$
+20240619	2025届高二10班	0.917
 
-041049
-$\dfrac59,\dfrac{5}{36}$
 
-004609
+004578
-(1)$\dfrac{25}{32}$\\
+20240619	2025届高二10班	0.700
-(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
+004572
-D
+20240619	2025届高二03班	1.000
 
-019245
-(1)$0.1\%$
-(2)$95.5\%$
 
-041153
+004573
-$\textcircled{3},\textcircled{4}$
+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
+004575
-$(0,\frac{1}{16})$;$y=-\frac{1}{16}$
+20240619	2025届高二03班	0.793
 
-021272
-$(0,-\frac{1}{6})$;$y=\frac{1}{6}$
 
-041007
+004576
-(1) $y^2=-x$; (2) $y^2=4x$或$y^2=-4x$或$x^2=-4y$或$x^2=4y$;\\
+20240619	2025届高二03班	0.951
-(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
+004577
-$(3,\pm 2\sqrt{3})$
+20240619	2025届高二03班	1.000
 
-021284
-$(3,\pm 2\sqrt{6})$
 
-021269
+004578
-A
+20240619	2025届高二03班	0.866
 
-021275
-$(\frac{m}{4},0)$;$x=-\frac{m}{4}$
 
-041008
+004572
-$(0,\frac{1}{4a})$;$y=-\frac{1}{4a}$
+20240619	2025届高二04班	0.971
 
-041009
-$y^2=12x$
 
-041010
+004573
-2
+20240619	2025届高二04班	0.971
 
-041011
-$y^2=-8x$;$m=\pm 2\sqrt{6}$
 
-008929
+004574
-$x^2=-y,x\in [-1,1]$
+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
+004575
-$(1,\pm 2)$
+20240619	2025届高二04班	0.571
 
-041013
-最小值为4, $M(\frac{1}{4},1)$
 
-041014
+004576
-$x^2=-12y$
+20240619	2025届高二04班	1.000
 
-021280
-$y^2=x$
 
-041015
+004577
-$y^2=8x$
+20240619	2025届高二04班	1.000
 
-021304
-$\frac{\pi}{2}$
 
-021308
+004578
-$\frac{11}{2}$
+20240619	2025届高二04班	0.657
 
-021287
-$\frac{45}{8}$
 
-009840
+004572
-$(\frac{1}{4},0)$;$x=-\frac{1}{4}$
+20240619	2025届高二05班	0.951
 
-021309
-2
 
-021290
+004573
-$(\frac{1}{2},1)$
+20240619	2025届高二05班	0.780
 
-021291
-$y^2=2x$或$y^2=6x$
 
-041016
+004574
-相切
+20240619	2025届高二05班	0.951
 
-021339
-$x^2-x+y^2=0(x\neq 0)$
 
-021289
+004575
-$4\sqrt{3}$
+20240619	2025届高二05班	0.585
 
-021293
-3
 
-021294
+004576
-$(4,2)$
+20240619	2025届高二05班	0.805
 
-021295
-$-4$
 
-021305
+004577
-$y^2=\pm 4x$
+20240619	2025届高二05班	1.000
 
-013106
-$[-1,1]$
 
-021292
+004578
-B
+20240619	2025届高二05班	0.927
 
-008930
-$0$或$-\frac{1}{2}$
 
-008934
+004572
-$4x-y-15=0$
+20240619	2025届高二07班	1.000
 
-008922
-$y=\frac{1}{4},x>\frac{1}{16}$
 
-021299
+004573
-2
+20240619	2025届高二07班	0.930
 
-021300
-$2\sqrt{15}$
 
-021321
+004574
-(1) 定点$(2,0)$;(2) 4
+20240619	2025届高二07班	0.860
 
-041017
-(1) 6; (2) $\frac{1}{32}$
 
-041018
+004575
-8
+20240619	2025届高二07班	0.616
 
-021316
-$\frac{11}{4}$
 
-021326
+004576
-8
+20240619	2025届高二07班	0.860
 
-021319
-$y=\pm \frac{\sqrt{3}}{3}x+1$
 
-041019
+004577
-$\frac{2}{p}$
+20240619	2025届高二07班	1.000
 
-041020
-D
 
-041021
+004578
-(1) $\frac{5p}{8}$; (2) $-2$;$-\frac{p}{y_0}$
+20240619	2025届高二07班	0.721
 
-021331
-D
 
-041022
+004572
-C
+20240619	2025届高二09班	0.914
 
-041023
-必要不充分
 
-021334
+004573
-$y=2x-3,x \leq 2$; $y=2x-3,x \in [1,2]$
+20240619	2025届高二09班	0.971
 
-021335
-$y=-2x^2+8x-4$
 
-021336
+004574
-$y^2=8x-16$
+20240619	2025届高二09班	0.886
 
-021337
-$x^2+y^2=1$
 
-021338
+004575
-$3x+y-4=0(x \neq 1)$
+20240619	2025届高二09班	0.729
 
-021340
-$(x-1)^2+(y-2)^2=\frac{1}{9}$
 
-021341
+004576
-$x+2y-5=0$
+20240619	2025届高二09班	0.914
 
-021342
-$x^2+y^2=4(x>0,y>0)$
 
-021343
+004577
-$(x-3)^2=10y-15$
+20240619	2025届高二09班	0.929
 
-041024
-C
 
-008846
+004578
-0或$-\frac{1}{2}$
+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$0<k<1$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$6000\sqrt{3}$