ans

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) $\overrightarrow{d}=(0,3 \sqrt{2}, 8)$.

041041
(1) 平面 $AA_1D_1D$.\\
(2) 平面 $BB_1D_1D$.

010793
(1)$\dfrac34$\\(2)变大

041042
(1)$y=4x-2$\\(2)$[\dfrac{\pi}{4},\dfrac{\pi}{2})$

022023
(1)$(2,4)$\\(2)$(-\dfrac32,\dfrac94)$\\(3)$(\dfrac12,\dfrac14)$

022025
$x=k\pi,k\in \mathbb{Z}$

041043
$\dfrac{\sqrt{2}}{2}$

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)$y'=\dfrac{1}{x\ln {10}}$

041047
$1-\dfrac{\sqrt{2}}{2}$

041048
$-\dfrac13,\dfrac{13}{6}$

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$p=\dfrac13$

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

019245
(1)$0.1\%$
(2)$95.5\%$

041153
$\textcircled{3},\textcircled{4}$

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''


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$6000\sqrt{3}$