ans

024871
B

024872
A

024873
D

024874
$[\dfrac{1}{2},1]$

024875
$[-1,0)\cup (3,4)$

024876
$\{(2,3)\}$

024877
D

024878
A

024879
D

024880
$3$

024881
$a\le \dfrac{1}{3}$

024882
$a\ge \dfrac{1}{5}$

024883
$\{a_2,a_4\}$, $\{a_1,a_2,a_4\}$, $\{a_2,a_3,a_4\}$, $\{a_1,a_2,a_3,a_4\}$

024884
$\{0,1\}$

024885
$(-\infty,-1]\cup \{1\}$

024886
\textcircled{4}

024887
B

024888
C

024889
充分非必要条件, 理由略

024890
(1) 证明略; (2) 证明略

024891
(1) $(1,+\infty)$; (2) $[-3,1]$

024892
$-3b^2$

024893
$1.82$

024894
$3$或$\dfrac{1}{3}$

024895
$(1,5)$

024896
$-1$

024897
$(-\infty,2]$

024898
$\dfrac{5}{2}$

024899
$2$

024900
$(2,5)$

024901
$3$

024902
C

024903
$[-6,1]$

024904
(1) $f(x)=\begin{cases}
\log_2 \dfrac{1}{x}, & x>0, \\ 0, & x=0, \\ -\log_2(-\dfrac{1}{x}), & x<0;
\end{cases}$ (2) 解集为$(-\log_2 3,+\infty)$

024905
(1) $(-\infty,-1]\cup [3,+\infty)$; (2) $(-\infty,3]$

024906
(1) $(-\infty,-\dfrac{3}{4}]$; (2) $\sqrt{3}$

024907
$-\dfrac{27}{19}$

024908
B

024909
$(1,\dfrac{3}{2}]$

024910
(1) $y=\begin{cases}
4t, & 0\le t<1, \\ (\dfrac{1}{2})^{t-3}, & t\ge 1;
\end{cases}$ (2) $\dfrac{79}{16}$

024911
$[\dfrac{1}{2},\dfrac{7}{2}]$

024912
(1) 证明略; (2) $(1,\dfrac{3}{2}]\cup \{2,3\}$

024913
D

024914
B

024915
C

024916
$\dfrac{1}{100}$

024917
$2$

024918
C

024919
A

024920
D

024921
C

024922
$(0,1]$

024923
$5$

024924
B

024925
$(-\infty,2]$

024926
(1) \begin{tikzpicture}[>=latex, scale = 0.6]
\draw [->] (-4,0) -- (4,0) node [below] {$x$};
\draw [->] (0,-5) -- (0,5) node [left] {$y$};
\draw (0,0) node [above left] {$O$};
\draw (-2,0) node [below left] {$-2$} (2,0) node [below right] {$2$} (0,-2) node [above right] {$-2$} (0,2) node [below right] {$2$} (0,4) node [below right] {$4$};
\foreach \i in {-5,-4,-3,-2,-1,1,2,3,4,5}
{\draw [dashed] (-4,\i) -- (4,\i);};
\foreach \i in {-4,-3,-2,-1,1,2,3,4}
{\draw [dashed] (\i,-5) -- (\i,5);};
\draw [domain = {-1-sqrt(6)}:0, samples = 100] plot (\x,{\x*(\x+2)});
\draw [domain = 0:{1+sqrt(6)}, samples = 100] plot (\x,{-\x*(\x-2)});
\end{tikzpicture} (2) $f(x)=-x^2+2x$($x>0$); (3) $(-1,1)$

024927
$(1,+\infty)$

024928
C

024929
C

024930
$-4$; $8$

024931
(1) $k=1$; (2) $Q(x)=125-|x-25|$($1\le x\le 30$, $x\in \mathbf{N}$); (3) $121$

024932
$(\dfrac{1}{3},-\dfrac{29}{27})$

024933
$0$; $(0,2)$

025063
B

025064
$\dfrac{2\sqrt{2}}{3}$

025065
$5$

025066
$-\dfrac{23}{16}$

025067
C

025068
B

025069
$-\dfrac{60}{169}$; $-\dfrac{12}{5}$

025070
$\dfrac{1}{3}$

025071
$\dfrac{7}{25}$

025072
B

025073
A

025074
D

025075
存在, $\alpha=\dfrac{\pi}{4}$, $\beta=\dfrac{\pi}{6}$

013851
(1) $28.28$米; (2) $26.93$米

025076
\textcircled{1}\textcircled{3}

025077
\textcircled{1}\textcircled{2}\textcircled{4}

025078
若选择\textcircled{1}, $a=8$, $b=3$; 若选择\textcircled{2}, $a=6$, $b=5$

025079
$2+\dfrac{3\sqrt{2}}{2}$

025080
C

025081
(1) $\sqrt{6}+\sqrt{2}$; (2) 证明略; (3) 当$a>2R$或$a=b=2R$时, $\triangle ABC$不存在; 当$b<a=2R$时, $\triangle ABC$有且仅有一个, $c=\sqrt{a^2-b^2}$; 当$b=a<2R$时, $\triangle ABC$有且仅有一个, $c=\dfrac{a}{R}\sqrt{4R^2-a^2}$; 当$b<a<2R$时, $\triangle ABC$有且仅有两个, $c=\sqrt{a^2+b^2\pm \dfrac{ab}{2R^2}(\sqrt{4R^2-a^2}\cdot \sqrt{4R^2-b^2}-ab)}$

024934
B

024935
D

024936
C

024937
B

024938
B

024939
$\dfrac{\sqrt{3}}{3}$

024940
$\dfrac{5\pi}{6}$

024941
C

024942
D

024943
B

024944
\textcircled{1}\textcircled{2}

024945
$\dfrac{\pi}{2}$

024946
(1) $\dfrac{\pi}{2}$; (2) 最大值为$3$, 当且仅当$x=\dfrac{\pi}{6}$时取到最大值; 最小值为$0$, 当且仅当$x=-\dfrac{\pi}{6}$时取到最小值

024947
(1) $[-\dfrac{\pi}{6},\dfrac{\pi}{3}]$和$[\dfrac{5\pi}{6},\pi]$; (2) 当$-2<a<-1$时, 方程无根; 当$-1<a\le 0$时, 方程有三个根; 当$a=-1$或$0<a<1$时, 方程有两个根

024948
(1) $[k\pi,k\pi+\dfrac{\pi}{2}]$, $k\in \mathbf{Z}$; (2) $-\dfrac{\sqrt{3}}{4}$

024949
\textcircled{2}\textcircled{3}\textcircled{4}

024950
D

024951
B

024952
(1) $\theta=\dfrac{\pi}{6}$, $\omega = 2$; (2) $x_0=\dfrac{2\pi}{3}$或$\dfrac{3\pi}{4}$


024953
(1) 存在$a=1$满足条件\textcircled{2}\textcircled{3}; (2) $(\dfrac{3\pi}{8},\dfrac{7\pi}{8}]$

024954
D

024955
D

024956
\textcircled{1}\textcircled{3}\textcircled{4}

024957
$\overrightarrow{AB}$

024958
$-\dfrac{5}{2}$

024959
$\dfrac{2\pi}{3}$

024960
C

024961
C

024962
D

024963
A

024964
B

024965
\begin{tikzpicture}[>=latex]
\draw (0,0) node [below right] {$A$} coordinate (A);
\draw (-1,0) node [below] {$B$} coordinate (B);
\draw (B) ++ (130:2) node [above] {$C$} coordinate (C);
\draw (C) ++ (1,0) node [above] {$D$} coordinate (D);
\draw (-2,0) node [below] {西} coordinate (l) -- (-1,0);
\draw [->] (0,0) -- (1,0) node [below] {东};
\draw [->] (0,-1) node [right] {南} -- (0,2) node [right] {北};
\draw (B) pic [draw, "$50^\circ$", scale = 0.5, angle eccentricity = 2.5] {angle = C--B--l};
\draw [->] (A)--(B);
\draw [->] (B)--(C);
\draw [->] (C)--(D);
\draw [->] (A)--(D);
\end{tikzpicture}

024966
(1) $\dfrac{1}{3}$; (2) $(-\dfrac{1}{2},\dfrac{1}{2})$

024967
(1) $(\sqrt{10},-2\sqrt{2})$或$(-\sqrt{10},2\sqrt{2})$; (2) $\dfrac{39}{8}$

024968
$14$; $10$

024969
$\dfrac{4}{3}$

024970
A

024971
(1) $\sqrt{3}$, $\dfrac{\sqrt{7}}{2}$; (2) 是定值$\dfrac{7}{8}$

032864
$\sqrt{7}$

024972
A

024973
D

024974
B

024975
D

024976
C

024977
B

024978
\textcircled{1}\textcircled{4}

024979
$\sqrt{2}$

024980
$-1$

024981
$\pm 4$

024982
B

024983
$5\sqrt{2}$; 一

024984
(1) $\dfrac{1}{2}$; (2) $(-\infty,-\dfrac{3}{2})$

024985
$-\dfrac{5}{3}$或$\dfrac{\sqrt{14}}{2}$

040763
$(x+y)(x-y)(x+y\mathrm{i})(x-y\mathrm{i})$

040764
$\dfrac{1}{12}$

024986
\textcircled{4}

024987
$\dfrac{3}{5}$或$\dfrac{5}{3}$或$-1$

024988
A

024989
$(-\infty,2-2\sqrt{2})\cup (2+\sqrt{2},+\infty)$

024990
$-10102$

024991
$(\dfrac{5}{4},\dfrac{10}{7}]$

024992
$-360$

024993
$68$

024994
$\begin{cases}
6n-1, & n\ge 2,\\ 6, & n=1
\end{cases}$

024995
$16$

024996
D

024997
$7$

024998
$\dfrac{3}{4}(9^n-1)$

024999
$\dfrac{4}{3}$

025000
$3^n-2$

025001
$-\dfrac{1}{2021}$

025002
(1) $a_n=\begin{cases}
\dfrac{1}{2}, & n=1, \\ 4, & n\ge 2;
\end{cases}$ (2) $T_n=2^{\frac{n(n-1)}{2}}$($n\in \mathbf{N}$, $n\ge 1$)

025003
有最大项, 最大项为$\dfrac{10^{10}}{11^9}$, 序数为$9$或$10$

025004
证明略

025005
B

025006
D

025007
(1) 证明略; (2) $(-\infty,-\dfrac{1}{3}]\cup [3,+\infty)$

025008
D

025009
$(-2,4)$

025010
$-6$

025011
$4$

025012
$\dfrac{1}{2}$

025013
$-\dfrac{\sqrt{3}}{3}$

025014
$2$

025015
$y=x-2$

025016
$4$

025017
$\dfrac{7\sqrt[8]{x^7}}{8x}$, $2\cos 2x$, $\dfrac{\mathrm{e}^x(x-1)}{x^2}$, $-\dfrac{1}{\sin^2 x}$, $\dfrac{2}{2x+1}-\mathrm{e}^{-x}(\cos 2x+2\sin 2x)$

025018
$-1$

025019
$[3,+\infty)$

025020
$(-\infty,0]\cup [3,+\infty)$

025021
$(-\dfrac{4}{3},\dfrac{28}{3})$

025022
$7.2$元, $20\mathrm{km}/\mathrm{h}$

025023
(1) $y=-4x+5$; (2) 在$(-\infty,-1]$和$[4,+\infty)$上严格增, 在$[-1,4]$上严格减, 最大值为$1$, 最小值为$-\dfrac{1}{4}$

025024
\textcircled{2}\textcircled{3}\textcircled{4}

025025
(1) $f'(x)=a\mathrm{e}^x\ln x+\dfrac{a\mathrm{e}^x}{x}+\dfrac{b\mathrm{e}^{x-1}x-b\mathrm{e}^{x-1}}{x^2}$; (2) $a=1$, $b=2$

025026
$1$

025027
$(-10,-2)$

025028
D

025029
(1) 最小值为$-\dfrac{1}{\mathrm{e}}$, 最大值为$0$; (2) $[1,+\infty)$

025030
$1$

025031
$\dfrac{1}{2}$

025032
$-\sqrt{3}$

025033
$[\dfrac{\pi}{12},\dfrac{\pi}{2}]$

025034
$2-\ln 2$

025035
$-6$

025036
$2$

025037
$\sqrt{3}$

025038
$\dfrac{\pi}{3}$

025039
C

025040
A

025041
B

025042
(1) $m=-4$, $n=5$; (2) $2\sqrt{3}$

025043
(1) $\pi-\arccos\dfrac{7\sqrt{19}}{38}$; (2) $(-\infty,-6)\cup (-6,\dfrac{7}{2})$

025044
(1) $AC=100\sqrt{7}$米, 原花园建筑用地$ABCD$的面积为$20000\sqrt{3}$平方米; (2) 当$\triangle ACP$为正三角形时, 新建筑用地面积最大, 最大值为$22500\sqrt{3}$平方米

019882
(1) $2$; (2) 定值为$6$, 证明略; (3) 存在, 最小值为$-2$

025045
(1) 极小值为$2-2\ln 2$, 无极大值; (2) 当$-2<a<0$时, 在$(0,\dfrac{1}{2}]$和$[-\dfrac{1}{a},+\infty)$上严格减, 在$[\dfrac{1}{2},-\dfrac{1}{a}]$上严格增; 当$a=-2$时, 在$(0,+\infty)$上严格减; 当$a<-2$时, 在$(0,-\dfrac{1}{a}]$和$[\dfrac{1}{2},+\infty)$上严格减, 在$[-\dfrac{1}{a},\dfrac{1}{2}]$上严格增; (3) $(-\infty,-\dfrac{13}{3}]$

025046
$\dfrac{\pi}{6}$

025047
$y=-x^{-2}$

025048
$-\dfrac{2\sqrt{6}}{5}$

011606
$2\sqrt{6}$

025049
$15$

025050
$y=-x+2$

025051
$\pi-\arccos\dfrac{1}{6}$

025052
$-2$

025053
\textcircled{1}

025054
$(-\dfrac{1}{\mathrm{e}},-0.02\ln 10)$

025055
$\dfrac{\sqrt{15}}{2}$

025056
C

025057
B

025058
A

014338
$(39,13)$

025059
(1) $f(x)=2\sin (2x+\dfrac{\pi}{3})$, 最小正周期为$\pi$; (2) $[-1,2]$

025060
(1) $\dfrac{100}{9}$; (2) $\dfrac{100}{7}$

025061
(1) $(0,\dfrac{1}{2}]$和$[2,+\infty)$; (2) $(-\infty,0)\cup \{1\}$; (3) 当$a=1$时, $f(x)$在$(0,+\infty)$上严格增; 当$a\in (0,1)$时, $f(x)$在$(0,a]$和$[\dfrac{1}{a},+\infty)$`上严格增, 在$(a,\dfrac{1}{a})$上严格减

025062
(1) 在$(0,+\infty)$上严格增; (2) $(-\infty,2+\dfrac{3}{\mathrm{e}}]$

025082
$\begin{cases}
1， & n=1,\\ -3, & n\ge 2
\end{cases}$

025083
B

025084
C

025085
(1) $\sqrt{26}$; (2) $-\dfrac{8}{13}$

025086
(1) 在$(0,+\infty)$上严格增; (2) $(\dfrac{5}{2},+\infty)$; (3) $[8-5\ln 2,+\infty)$