707 lines
9.1 KiB
Plaintext
707 lines
9.1 KiB
Plaintext
ans
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024871
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B
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024872
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A
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024873
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D
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024874
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$[\dfrac{1}{2},1]$
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024875
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$[-1,0)\cup (3,4)$
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024876
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$\{(2,3)\}$
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024877
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D
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024878
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A
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024879
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D
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024880
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$3$
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024881
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$a\le \dfrac{1}{3}$
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024882
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$a\ge \dfrac{1}{5}$
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024883
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$\{a_2,a_4\}$, $\{a_1,a_2,a_4\}$, $\{a_2,a_3,a_4\}$, $\{a_1,a_2,a_3,a_4\}$
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024884
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$\{0,1\}$
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024885
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$(-\infty,-1]\cup \{1\}$
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024886
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\textcircled{4}
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024887
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B
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024888
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C
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024889
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充分非必要条件, 理由略
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024890
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(1) 证明略; (2) 证明略
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024891
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(1) $(1,+\infty)$; (2) $[-3,1]$
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024892
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$-3b^2$
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024893
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$1.82$
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024894
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$3$或$\dfrac{1}{3}$
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024895
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$(1,5)$
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024896
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$-1$
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024897
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$(-\infty,2]$
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024898
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$\dfrac{5}{2}$
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024899
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$2$
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024900
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$(2,5)$
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024901
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$3$
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024902
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C
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024903
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$[-6,1]$
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024904
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(1) $f(x)=\begin{cases}
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\log_2 \dfrac{1}{x}, & x>0, \\ 0, & x=0, \\ -\log_2(-\dfrac{1}{x}), & x<0;
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\end{cases}$ (2) 解集为$(-\log_2 3,+\infty)$
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024905
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(1) $(-\infty,-1]\cup [3,+\infty)$; (2) $(-\infty,3]$
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024906
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(1) $(-\infty,-\dfrac{3}{4}]$; (2) $\sqrt{3}$
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024907
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$-\dfrac{27}{19}$
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024908
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B
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024909
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$(1,\dfrac{3}{2}]$
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024910
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(1) $y=\begin{cases}
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4t, & 0\le t<1, \\ (\dfrac{1}{2})^{t-3}, & t\ge 1;
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\end{cases}$ (2) $\dfrac{79}{16}$
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024911
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$[\dfrac{1}{2},\dfrac{7}{2}]$
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024912
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(1) 证明略; (2) $(1,\dfrac{3}{2}]\cup \{2,3\}$
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024913
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D
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024914
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B
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024915
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C
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024916
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$\dfrac{1}{100}$
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024917
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$2$
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024918
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C
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024919
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A
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024920
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D
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024921
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C
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024922
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$(0,1]$
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024923
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$5$
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024924
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B
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024925
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$(-\infty,2]$
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024926
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(1) \begin{tikzpicture}[>=latex, scale = 0.6]
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\draw [->] (-4,0) -- (4,0) node [below] {$x$};
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\draw [->] (0,-5) -- (0,5) node [left] {$y$};
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\draw (0,0) node [above left] {$O$};
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\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] {$4$};
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\foreach \i in {-5,-4,-3,-2,-1,1,2,3,4,5}
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{\draw [dashed] (-4,\i) -- (4,\i);};
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\foreach \i in {-4,-3,-2,-1,1,2,3,4}
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{\draw [dashed] (\i,-5) -- (\i,5);};
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\draw [domain = {-1-sqrt(6)}:0, samples = 100] plot (\x,{\x*(\x+2)});
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\draw [domain = 0:{1+sqrt(6)}, samples = 100] plot (\x,{-\x*(\x-2)});
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\end{tikzpicture} (2) $f(x)=-x^2+2x$($x>0$); (3) $(-1,1)$
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024927
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$(1,+\infty)$
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024928
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C
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024929
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C
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024930
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$-4$; $8$
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024931
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(1) $k=1$; (2) $Q(x)=125-|x-25|$($1\le x\le 30$, $x\in \mathbf{N}$); (3) $121$
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024932
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$(\dfrac{1}{3},-\dfrac{29}{27})$
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024933
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$0$; $(0,2)$
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025063
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B
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025064
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$\dfrac{2\sqrt{2}}{3}$
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025065
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$5$
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025066
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$-\dfrac{23}{16}$
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025067
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C
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025068
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B
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025069
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$-\dfrac{60}{169}$; $-\dfrac{12}{5}$
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025070
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$\dfrac{1}{3}$
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025071
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$\dfrac{7}{25}$
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025072
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B
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025073
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A
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025074
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D
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025075
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存在, $\alpha=\dfrac{\pi}{4}$, $\beta=\dfrac{\pi}{6}$
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013851
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(1) $28.28$米; (2) $26.93$米
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025076
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\textcircled{1}\textcircled{3}
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025077
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\textcircled{1}\textcircled{2}\textcircled{4}
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025078
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若选择\textcircled{1}, $a=8$, $b=3$; 若选择\textcircled{2}, $a=6$, $b=5$
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025079
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$2+\dfrac{3\sqrt{2}}{2}$
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025080
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C
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025081
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(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, $c=\sqrt{a^2+b^2\pm \dfrac{ab}{2R^2}(\sqrt{4R^2-a^2}\cdot \sqrt{4R^2-b^2}-ab)}$
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024934
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B
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024935
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D
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024936
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C
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024937
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B
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024938
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B
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024939
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$\dfrac{\sqrt{3}}{3}$
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024940
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$\dfrac{5\pi}{6}$
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024941
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C
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024942
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D
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024943
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B
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024944
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\textcircled{1}\textcircled{2}
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024945
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$\dfrac{\pi}{2}$
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024946
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(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
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024947
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(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
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024948
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(1) $[k\pi,k\pi+\dfrac{\pi}{2}]$, $k\in \mathbf{Z}$; (2) $-\dfrac{\sqrt{3}}{4}$
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024949
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\textcircled{2}\textcircled{3}\textcircled{4}
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024950
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D
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024951
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B
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024952
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(1) $\theta=\dfrac{\pi}{6}$, $\omega = 2$; (2) $x_0=\dfrac{2\pi}{3}$或$\dfrac{3\pi}{4}$
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024953
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(1) 存在$a=1$满足条件\textcircled{2}\textcircled{3}; (2) $(\dfrac{3\pi}{8},\dfrac{7\pi}{8}]$
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024954
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D
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024955
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D
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024956
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\textcircled{1}\textcircled{3}\textcircled{4}
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024957
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$\overrightarrow{AB}$
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024958
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$-\dfrac{5}{2}$
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024959
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$\dfrac{2\pi}{3}$
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024960
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C
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024961
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C
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024962
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D
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024963
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A
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024964
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B
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024965
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\begin{tikzpicture}[>=latex]
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\draw (0,0) node [below right] {$A$} coordinate (A);
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\draw (-1,0) node [below] {$B$} coordinate (B);
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\draw (B) ++ (130:2) node [above] {$C$} coordinate (C);
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\draw (C) ++ (1,0) node [above] {$D$} coordinate (D);
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\draw (-2,0) node [below] {西} coordinate (l) -- (-1,0);
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\draw [->] (0,0) -- (1,0) node [below] {东};
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\draw [->] (0,-1) node [right] {南} -- (0,2) node [right] {北};
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\draw (B) pic [draw, "$50^\circ$", scale = 0.5, angle eccentricity = 2.5] {angle = C--B--l};
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\draw [->] (A)--(B);
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\draw [->] (B)--(C);
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\draw [->] (C)--(D);
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\draw [->] (A)--(D);
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\end{tikzpicture}
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024966
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(1) $\dfrac{1}{3}$; (2) $(-\dfrac{1}{2},\dfrac{1}{2})$
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024967
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(1) $(\sqrt{10},-2\sqrt{2})$或$(-\sqrt{10},2\sqrt{2})$; (2) $\dfrac{39}{8}$
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024968
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$14$; $10$
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024969
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$\dfrac{4}{3}$
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024970
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A
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024971
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(1) $\sqrt{3}$, $\dfrac{\sqrt{7}}{2}$; (2) 是定值$\dfrac{7}{8}$
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032864
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$\sqrt{7}$
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024972
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A
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024973
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D
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024974
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B
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024975
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D
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024976
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C
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024977
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B
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024978
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\textcircled{1}\textcircled{4}
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024979
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$\sqrt{2}$
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024980
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$-1$
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024981
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$\pm 4$
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024982
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B
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024983
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$5\sqrt{2}$; 一
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024984
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(1) $\dfrac{1}{2}$; (2) $(-\infty,-\dfrac{3}{2})$
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024985
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$-\dfrac{5}{3}$或$\dfrac{\sqrt{14}}{2}$
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040763
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$(x+y)(x-y)(x+y\mathrm{i})(x-y\mathrm{i})$
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040764
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$\dfrac{1}{12}$
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024986
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\textcircled{4}
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024987
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$\dfrac{3}{5}$或$\dfrac{5}{3}$或$-1$
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024988
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A
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024989
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$(-\infty,2-2\sqrt{2})\cup (2+\sqrt{2},+\infty)$
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024990
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$-10102$
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024991
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$(\dfrac{5}{4},\dfrac{10}{7}]$
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024992
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$-360$
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024993
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$68$
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024994
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$\begin{cases}
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6n-1, & n\ge 2,\\ 6, & n=1
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\end{cases}$
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024995
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$16$
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024996
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D
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024997
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$7$
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024998
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$\dfrac{3}{4}(9^n-1)$
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024999
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$\dfrac{4}{3}$
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025000
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$3^n-2$
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025001
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$-\dfrac{1}{2021}$
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025002
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(1) $a_n=\begin{cases}
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\dfrac{1}{2}, & n=1, \\ 4, & n\ge 2;
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\end{cases}$ (2) $T_n=2^{\frac{n(n-1)}{2}}$($n\in \mathbf{N}$, $n\ge 1$)
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025003
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有最大项, 最大项为$\dfrac{10^{10}}{11^9}$, 序数为$9$或$10$
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025004
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证明略
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025005
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B
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025006
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D
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025007
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(1) 证明略; (2) $(-\infty,-\dfrac{1}{3}]\cup [3,+\infty)$
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025008
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D
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025009
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$(-2,4)$
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025010
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$-6$
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025011
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$4$
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025012
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$\dfrac{1}{2}$
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025013
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$-\dfrac{\sqrt{3}}{3}$
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025014
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$2$
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025015
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$y=x-2$
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025016
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$4$
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025017
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$\dfrac{7\sqrt[8]{x^7}}{8x}$, $2\cos 2x$, $\dfrac{\mathrm{e}^x(x-1)}{x^2}$, $-\dfrac{1}{\sin^2 x}$, $\dfrac{2}{2x+1}-\mathrm{e}^{-x}(\cos 2x+2\sin 2x)$
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025018
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$-1$
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025019
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$[3,+\infty)$
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025020
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$(-\infty,0]\cup [3,+\infty)$
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025021
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$(-\dfrac{4}{3},\dfrac{28}{3})$
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025022
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$7.2$元, $20\mathrm{km}/\mathrm{h}$
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025023
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(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$-\dfrac{1}{4}$
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025024
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\textcircled{2}\textcircled{3}\textcircled{4}
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025025
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(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) $a=1$, $b=2$
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025026
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$1$
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025027
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$(-10,-2)$
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025028
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D
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025029
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(1) 最小值为$-\dfrac{1}{\mathrm{e}}$, 最大值为$0$; (2) $[1,+\infty)$
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025030
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$1$
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025031
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$\dfrac{1}{2}$
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025032
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$-\sqrt{3}$
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025033
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$[\dfrac{\pi}{12},\dfrac{\pi}{2}]$
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025034
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$2-\ln 2$
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025035
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$-6$
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025036
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$2$
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025037
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$\sqrt{3}$
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025038
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$\dfrac{\pi}{3}$
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025039
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C
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025040
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A
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025041
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B
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025042
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(1) $m=-4$, $n=5$; (2) $2\sqrt{3}$
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025043
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(1) $\pi-\arccos\dfrac{7\sqrt{19}}{38}$; (2) $(-\infty,-6)\cup (-6,\dfrac{7}{2})$
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025044
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(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) $[8-5\ln 2,+\infty)$
|
||
|