1825 lines
21 KiB
Plaintext
1825 lines
21 KiB
Plaintext
ans
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018366
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(1) $x=\dfrac{\pi}{3}+2k\pi$或$\dfrac{2\pi}{3}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{3\pi}{4}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$
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018367
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(1) $\{\dfrac{\pi}{6},\dfrac{\pi}{3},\dfrac{7\pi}{6},\dfrac{4\pi}{3}\}$; (2) $\{x|x=2k\pi+\dfrac{\pi}{12}\text{或}x=2k\pi-\dfrac{5\pi}{12}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{2}+\dfrac{\pi}{4}, \ k\in \mathbf{Z}\}$
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018369
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(1) $x=-\dfrac{\pi}{2}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{\pi}{6}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$
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009563
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(1) $\{\dfrac{\pi}{2},\dfrac{11\pi}{6}\}$; (2) $\{x|x=k\pi+\dfrac{5\pi}{24}\text{或}k\pi-\dfrac{11\pi}{24}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{3}+\dfrac{\pi}{6}, \ k\in \mathbf{Z}\}$
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018372
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$\dfrac{\sqrt{6}-\sqrt{2}}{4}$, $\dfrac{\sqrt{6}+\sqrt{2}}{4}$
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018373
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$-\dfrac{56}{65}$
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018375
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$\dfrac{\pi}{3}$
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009564
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(1) $\dfrac{\sqrt{2}}{2}$; (2) $\dfrac{\sqrt{3}}{2}$
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009565
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$-\dfrac{7\sqrt{2}}{26}$
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018377
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(1) $\dfrac{\sqrt{3}}{2}$; (2) $\cos 2\alpha$; (3) $-\cos 3x$
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018376
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$-\dfrac{4}{5}$
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018378
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$\dfrac{\sqrt{6}-\sqrt{2}}{4}$
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018379
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证明略
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018380
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(1) $-1$; (2) $\dfrac{1}{7}$
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018381
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$-\sqrt{3}$
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009567
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(1) $\dfrac{\sqrt{3}}{2}$; (2) $\sqrt{3}$
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009568
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$\dfrac{\sqrt{2}}{10}$, $7$
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009569
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(1) 证明略; (2) 证明略
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018385
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证明略
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018386
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$(-\dfrac{\sqrt{2}}{2},\dfrac{3\sqrt{2}}{2})$
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018387
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(1) $\sin(\alpha+\dfrac{\pi}{3})$; (2) $\sqrt{2}\sin(\alpha-\dfrac{\pi}{4})$; (3) $5\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{3}{5}$, $\sin\varphi=\dfrac{4}{5}$; (4) $\sqrt{a^2+b^2}\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{a}{\sqrt{a^2+b^2}}$, $\sin\varphi=\dfrac{b}{\sqrt{a^2+b^2}}$
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024614
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$\{\alpha|\alpha=2k\pi\text{或}\dfrac{2\pi}{3}+2k\pi, \ k\in \mathbf{Z}\}$
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009570
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$\sin C=\dfrac{220}{221}$, $\cos C=-\dfrac{21}{221}$
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009571
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$\sin(\alpha+\beta)=\dfrac{33}{65}$, $\cos(\alpha+\beta)=-\dfrac{56}{65}$, $\alpha+\beta$是第二象限角
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009572
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(1) $\sqrt{2}\sin(\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha+\dfrac{2\pi}{3})$
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018390
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$\dfrac{\sqrt{6}-\sqrt{2}}{4}$
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018402
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证明略
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018403
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证明略
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018404
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证明略
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009576
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证明略
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009577
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证明略
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009578
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证明略
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018405
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证明略
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040387
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$\dfrac{5\pi}{3}$
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040388
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$-1$
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040389
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$-\dfrac{\pi}{3}$或$\dfrac{4\pi}{3}$
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040390
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$-3$
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040391
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$-2$
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040392
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$-\dfrac{\sqrt{23}}{4}$
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ans
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041050
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$2\sqrt{7}$, $(0,\pm \sqrt{7})$
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040971
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$2\sqrt{7}$, $(\pm \sqrt{7},0)$
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041051
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D
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040972
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$x=0(-3 \leq y \leq 3)$
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040973
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B
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040974
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$\dfrac{x^2}7+\dfrac{y^2}{16}=1$
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040975
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B
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008878
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D
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008877
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A
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014470
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$4\sqrt{3}$
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040976
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$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}7+\dfrac{y^2}{16}=1$
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040977
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(1)$\dfrac{x^2}{100}+\dfrac{y^2}{64}=1$;
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(2)$\dfrac{x^2}6+\dfrac{y^2}4=1$
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040978
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(1)$k=7$;(2)$4<k<7$
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040979
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$5$,$8$,$6$,$\dfrac35$
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008882
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$(0,\pm5)$
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021195
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$20$
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021196
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$\dfrac{x^2}{15}+\dfrac{y^2}{10}=1$
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040980
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$\dfrac{x^2}{\dfrac{625}{16}}+\dfrac{y^2}{34}=1$
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040981
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$\dfrac35$
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040982
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$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}{16}+\dfrac{y^2}{25}=1$
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008892
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$\dfrac{x^2}9+\dfrac{y^2}{16}=1$
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040983
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$18$
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040984
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$1$
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040985
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(1)$10$;(2)$2$
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040986
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(1)$\dfrac{x^2}4+\dfrac{y^2}{8}=1$或$\dfrac{x^2}8+\dfrac{y^2}{4}=1$;\\
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(2)$\dfrac{x^2}6+\dfrac{y^2}{10}=1$;\\
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(3)$\dfrac{x^2}8+\dfrac{y^2}{32}=1$或$\dfrac{x^2}{68}+\dfrac{y^2}{17}=1$;\\
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(4)$\dfrac{x^2}{40}+\dfrac{y^2}{4}=1$或$\dfrac{x^2}{36}+\dfrac{y^2}{40}=1$;\\
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(5)$\dfrac{x^2}{10}+\dfrac{y^2}{5}=1$
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021183
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C
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008883
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D
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040987
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$\dfrac{x^2}{16}+\dfrac{y^2}{8}=1$
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040988
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$\dfrac{x^2}{10}+\dfrac{y^2}{5}=1(y\neq 0)$
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040989
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$2$,$\dfrac{2\pi}{3}$
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008895
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B
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040990
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$\dfrac{x^2}{4}+\dfrac{y^2}{3}=1(-2<x<0)$
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040991
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A
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040992
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$\dfrac{x^2}{36}+\dfrac{y^2}{16}=1(y \neq 0)$
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008898
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$\dfrac{x^2}{16}+\dfrac{y^2}{7}=1$
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040993
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$32-16\sqrt{3}$
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008891
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(1)$15$,$5$;(2)$(\dfrac{25}4,\pm \dfrac{3\sqrt{39}}{4})$
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021197
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$x\pm2\sqrt{6}y-5=0$
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021184
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$(-\sqrt{3},\sqrt{3})$
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021185
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$[\sqrt{2},\sqrt{3})$
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021186
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$[1,5)\cup(5,+infty)$
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021187
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$\sqrt{2}-1$
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021198
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$4x+9y-13=0$
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021188
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$(x-3)^2+(y-4)^2=4$
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040994
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$4$
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021190
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$(-\sqrt95,\sqrt15)$
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021191
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$k<-\sqrt{3}$或$k>\sqrt{3}$
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040995
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(1)$y=-\sqrt12+\sqrt34$;(2)$x+4y=0$(点在已知椭圆内);(3)$x^2+x+2y^2=0$
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040996
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$6\sqrt{5}$
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021204
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$\dfrac{\sqrt{2}}{2}$
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021205
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$2\sqrt{37}$,$2$
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021206
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$\dfrac{x^2}{25}+\dfrac{y^2}{75}=1$
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021207
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$\dfrac{x^2}{12}+\dfrac{y^2}{9}=1$或$\dfrac{x^2}{9}+\dfrac{y^2}{12}=1$
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021208
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$[-\sqrt{34},\sqrt{34}]$
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021209
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$\dfrac{\pi}3$
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040997
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$b\sqrt{a^2-b^2}$
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040998
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$8\sqrt{3}$
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021212
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$P(-6,-4)$,$d=\dfrac{22}{\sqrt{73}}$
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021200
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$\dfrac{x^2}{4}+y^2=1$
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021201
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$-\dfrac{5\sqrt{7}}{4}<x<\dfrac{5\sqrt{7}}{4}$
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021202
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$-\dfrac{2\sqrt{13}}{13}<m<\dfrac{2\sqrt{13}}{13}$
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021203
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(1)$\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$;(2)$8x-9y+25=0$
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040999
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(1)$-6$;(2)$\dfrac{x^2}{a^2}-\dfrac{y^2}{ta^2}=1(x\neq \pm a)$;(3)$\dfrac{\sqrt{6}}{3}$;(4)$\dfrac{\sqrt{6}}{3}$或$\sqrt{6}$
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041000
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C,A,A
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021222
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(1)$\dfrac{x^2}{9}-\dfrac{y^2}{7}=1$;(2)$\dfrac{y^2}{64}-\dfrac{x^2}{36}=1(y>0)$;(3)$x^2-\dfrac{y^2}{3}=1$
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021223
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$\dfrac{x^2}{20}-\dfrac{y^2}{16}=1$
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021224
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$\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$
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021225
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不正确, 正确结果为$17$
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021226
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$\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$
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021227
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D
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021228
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$(-3,6)$
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021229
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$m<-2$
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021230
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$\dfrac{41}{4}$
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021231
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$32+2m$
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021232
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$|PF_1|=\dfrac{c}{a}x_0+a$,$|PF_2|=\dfrac{c}{a}x_0-a$
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021233
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$x^2-\dfrac{y^2}{4}=1$
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041001
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(1)$\dfrac{y^2}{18}-\dfrac{x^2}{18}=1$,$\sqrt{2}$;(2)$(\pm 2\sqrt{3},0)$,$\arctan{2\sqrt{2}}$
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041002
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A,A,B,B
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041003
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(1))$\dfrac{x^2}{3}-\dfrac{y^2}{5}=1$;(2))$\dfrac{y^2}{81}-\dfrac{x^2}{9}=1$或)$x^2-\dfrac{y^2}{9}=1$
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021242
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$\dfrac{x^2}{3}-\dfrac{y^2}{12}=1$
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021243
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$y=\pm \dfrac{\sqrt{2}}{4}x$
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021244
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证明略
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041004
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(1)$\dfrac{x^2}{\dfrac{81}{13}}-\dfrac{y^2}{\dfrac{36}{13}}=1$;(2)$2$或$\dfrac{2\sqrt{3}}{3}$; (3)$(\dfrac 52,\dfrac 72)$;(4)$(\pm \sqrt{7},0)$
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041005
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D,A,D
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021251
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$a^2$
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021263
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$\dfrac{y^2}{36}-\dfrac{x^2}{81}=1(x\neq 0)$
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021252
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$\dfrac{c}{a}$
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021253
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$y=\pm \sqrt{2}x$
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021254
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$0$
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008917
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$\dfrac{x^2}{4}-\dfrac{y^2}{5}=1$(x>0)
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021255
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$\dfrac{2\sqrt{3}}{3}$
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021256
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$\dfrac{14\sqrt{3}}{3}$
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041006
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$3$
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021258
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$x^2-4y^2=\pm \dfrac{36}{5}$
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021259
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$(-\dfrac{\sqrt{15}}{3},-1)$
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021260
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(1)椭圆:$k<4$,双曲线: $4<k<9$;(2)$\dfrac{x^2}{3}-\dfrac{y^2}{2}=1$
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021261
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(1)$(\sqrt{6},-\sqrt{3})\cup(\sqrt{3},\sqrt{3})\cup(\sqrt{3},\sqrt{6})$;(2)$\pm 1$
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021267
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(1)$e>\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$
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ans
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012360
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$\dfrac{\pi}{3}$
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009305
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(1)$x^15$,$-15x^14$,$105x^13$,$-455x^12$\\
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(2)$-2099520a^9b^14$
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009306
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(1)$\dfrac{105}{8}$;(2)$-252$
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009309
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$120$
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009308
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证明略
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009317
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(1)第$18$,$19$项; \\
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(2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$
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009319
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证明略
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021093
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(1)$\dfrac{1}{45}$;(2)$\dfrac{7}{10}$
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022919
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(1)$\dfrac{1}{36}$;(2)$\dfrac{1}{18}$;(3)$\dfrac{5}{12}$
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021095
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(1)$\dfrac{1}{68880}$;(2)$\dfrac{1}{11480}$
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021096
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$\dfrac37$
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021097
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$\dfrac{1}{12}$
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021098
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$\dfrac{18}{25}$
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021099
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$\dfrac{2}{5}$
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021101
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$\dfrac{11}{12}$
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021102
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$\dfrac{3439}{10000}$
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021103
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$\dfrac{n!}{n^n}$
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021104
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$\dfrac{1}{15}$
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021105
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$\dfrac15$
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021106
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(1)$\dfrac{11}{42}$;(2)$\dfrac{31}{42}$
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021107
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(1)$\dfrac{1279}{1785}$;(2)$\dfrac{59049}{139075300}$
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021108
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(1)$\{5,7,9\}$;(2)$\{0,2,4,5,6,7,8,9\}$;(3)$\emptyset$
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021109
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B
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021110
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(1)$\{1,2,3,4\}$;(2)A
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021111
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(1)$\{1,2,3,4\}$;(2)A
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021112
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充分非必要
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021113
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(1)$A\cup B$;(2)$A \cap \overline{B}$;(3)$(A \cap \overline{B}) \cup(\overline{A} \cap B) $
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021114
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$B\subseteq \overline{A}$,$\overline{A}\cup \overline{B}=\omega$
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021116
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(1)$\dfrac12$;(2)$\dfrac56$;(3)$\dfrac23$;(4)$\dfrac56$
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021117
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(1)不是;(2)$0.94$
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021125
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(1)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)\cup (A \cap B \cap C)$;
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(2)$\overline{A\cap B \cap C }$;
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(3)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)$
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021118
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$\dfrac47$,$\dfrac27$,$\dfrac17$,$\dfrac67$,$\dfrac67$,$\dfrac57$
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019932
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(1)$\dfrac34$;(2)$\dfrac1{13}$;(3)$\dfrac12$;(4)$\dfrac{51}{52}$
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021119
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$\dfrac45$
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021120
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$\dfrac35$
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021121
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$\dfrac14$,$\dfrac16$,$\dfrac14$
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021122
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$0.9$,$0.1$
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018762
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证明略
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021126
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大数定律
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021127
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$\dfrac{73}{75}$
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021128
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$\dfrac34$,$\dfrac{9}{44}$,$\dfrac{9}{220}$.$\dfrac{1}{220}$
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021129
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(1)$0.46$;(2)$0.51$;(3)$0.97$
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021130
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(1)$0.852$;(2)$25560$;(3)$5869$
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021131
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(1)$0.1,0.06,0.025,0.02,0.02,0.02$;(2)$0.02$;(3)$40$
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021132
|
|
(1)$30\%$;(2)$53\%$;(3)$73\%$;(4)$14\%$;(5)$90\%$;(6)$10\%$;
|
|
|
|
021133
|
|
(1)$\dfrac13$;(2)$\dfrac14$
|
|
|
|
021134
|
|
C
|
|
|
|
021135
|
|
(1)$\dfrac56$;(2)$\dfrac16$;(3)$\dfrac23$;(4)$\dfrac12$
|
|
|
|
021136
|
|
(1)$0.995$;(2)$0.095$
|
|
|
|
021137
|
|
(1)$7:1$;(2)$11:5$
|
|
|
|
021138
|
|
$0.328$
|
|
|
|
021139
|
|
$(\dfrac23,1)$
|
|
|
|
021140
|
|
(1)$\dfrac38$,$\dfrac23$;(2)$\dfrac{21}{32}$
|
|
|
|
021141
|
|
D
|
|
|
|
021142
|
|
D
|
|
|
|
021143
|
|
A
|
|
|
|
021144
|
|
A
|
|
|
|
021145
|
|
\textcircled{2}
|
|
|
|
021146
|
|
总体是$2487$万人的年龄, 样本是$24000$个常住居民的年龄, 样本量是$24000$
|
|
|
|
021147
|
|
观测, 观测, 实验
|
|
|
|
021148
|
|
不可靠, 样本容量太小, 样本不一定具有代表性
|
|
|
|
021149
|
|
$2$
|
|
|
|
021150
|
|
$122$
|
|
|
|
021151
|
|
$a=b=10.5$
|
|
|
|
021152
|
|
平均值是$17$,方差是$27$
|
|
|
|
021153
|
|
平均数是$72.0$, 中位数是$70$, 方差是$74.9$
|
|
|
|
021154
|
|
$\dfrac{n}{N}$
|
|
|
|
021155
|
|
B
|
|
|
|
021156
|
|
20
|
|
|
|
021157
|
|
C
|
|
|
|
021158
|
|
$4467$
|
|
|
|
021159
|
|
(1)抽签法;(2)分层抽样
|
|
|
|
021160
|
|
$49,04,40,36,16,08,06,55,33,69$
|
|
|
|
021161
|
|
样本容量为$92$, 抽样人数为$31$
|
|
|
|
021162
|
|
略
|
|
|
|
021163
|
|
分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人
|
|
|
|
021164
|
|
C
|
|
|
|
021165
|
|
$4$,$5.14$
|
|
|
|
021166
|
|
$0.32$,$96$
|
|
|
|
021167
|
|
$300$
|
|
|
|
021168
|
|
集中, 分散, $6.88$,$12.43$
|
|
|
|
021169
|
|
\begin{tabular}{c|ccccccc}
|
|
8 & 9 \\
|
|
9 & 3 & 4 & 6 & 7 \\
|
|
10 & 0 & 0 & 1 & 1 & 3 & 5 & 8\\
|
|
11 & 0 & 2
|
|
\end{tabular}
|
|
|
|
021170
|
|
略
|
|
|
|
021171
|
|
略
|
|
|
|
021172
|
|
D
|
|
|
|
021173
|
|
$35$
|
|
|
|
021174
|
|
$12$
|
|
|
|
021177
|
|
C
|
|
|
|
021179
|
|
\textcircled{1},\textcircled{2}
|
|
|
|
021180
|
|
A
|
|
|
|
021175
|
|
甲更准, 乙更稳定
|
|
|
|
021176
|
|
(1)$3.47$,(2)$2773$
|
|
|
|
021178
|
|
$100$
|
|
|
|
021181
|
|
(1)$9.5$;(2)不能
|
|
|
|
021182
|
|
平均成绩是$89.6$, 总体方差是$12.09$
|
|
|
|
023356
|
|
$A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$
|
|
|
|
023357
|
|
全错
|
|
|
|
023358
|
|
$\dfrac{72\sqrt{21}}7$
|
|
|
|
023359
|
|
(1)$\dfrac16$;(2)
|
|
|
|
023360
|
|
$2\sqrt{15}$或$4\sqrt{6}$
|
|
|
|
023361
|
|
略
|
|
|
|
023362
|
|
$\frac{b^2-a^2}{\sqrt{a^2+b^2} \cdot \sqrt{a^2+b^2+c^2}}$.
|
|
|
|
023363
|
|
(1) $\frac{1}{2}$; (2) $\frac{\pi}{3}$.
|
|
|
|
023364
|
|
(1) 略; (2) $\arcsin{\frac{3\sqrt{2}}{10}}$; (3) $\frac{24\sqrt{41}}{41}$
|
|
|
|
023365
|
|
略
|
|
|
|
023366
|
|
$\sqrt{41}$
|
|
|
|
023367
|
|
(1) 略; (2) $\frac{\pi}{4}$.
|
|
|
|
023368
|
|
$8\sqrt{3}$.
|
|
|
|
003494
|
|
(1) 略; (2) $3$; (3) $108\sqrt{3}$.
|
|
|
|
023369
|
|
(1) $48$; (2) $16\sqrt{3}+8\sqrt{21}+40$
|
|
|
|
023370
|
|
(1) 略; (2) $\frac{1}{3}$; (3) $\frac{\sqrt{2}}{2}+\frac{\sqrt{6}}{2}$.
|
|
|
|
023108
|
|
C
|
|
|
|
023109
|
|
1; 4.
|
|
|
|
023110
|
|
8; 4.
|
|
|
|
023111
|
|
$M \in a$,$M \notin \alpha$.
|
|
|
|
023112
|
|
$\{1,4,6\}$.
|
|
|
|
023113
|
|
$D$.
|
|
|
|
023114
|
|
$C$.
|
|
|
|
023115
|
|
$A$.
|
|
|
|
023116
|
|
1个或者无数个
|
|
|
|
023117
|
|
平行四边形
|
|
|
|
023118
|
|
10
|
|
|
|
023119
|
|
\textcircled{1}, \textcircled{2} ,\textcircled{4}, \textcircled{5}.
|
|
|
|
023120
|
|
$D$.
|
|
|
|
012345
|
|
$D$.
|
|
|
|
023124
|
|
$\frac{5(\sqrt{6}-1)}{2} $.
|
|
|
|
023125
|
|
$\sqrt{2}+2\sqrt{13}$.
|
|
|
|
023126
|
|
(1) F ; (2) F; (3) F; (4) T; (5) T; (6) T; (7) T; (8) F.
|
|
|
|
023127
|
|
(1) T ; (2) F; (3) F; (4) F; (5) F.
|
|
|
|
023128
|
|
异面或者平行.
|
|
|
|
023129
|
|
(1) 平行; (2) 异面.
|
|
|
|
023130
|
|
相交或者平行.
|
|
|
|
023131
|
|
充分不必要.
|
|
|
|
023132
|
|
4个.
|
|
|
|
023133
|
|
$45^{\circ}$; $30^{\circ}$或$60^{\circ}$.
|
|
|
|
023134
|
|
(1) $\frac{\pi}{3}$; (2) $\arccos \frac{\sqrt{10}}{10}$; (3) $\arccos \frac{\sqrt{10}}{5}$.
|
|
|
|
023135
|
|
\textcircled{1} \textcircled{4}.
|
|
|
|
023136
|
|
$\frac{a}{3}$.
|
|
|
|
012345
|
|
D
|
|
|
|
023137
|
|
B
|
|
|
|
023140
|
|
$\frac{\pi}{4}$或$\frac{\pi}{3}$.
|
|
|
|
023141
|
|
(1) 点 $P$ 在$C$点; (2) 点 $P$ 在距离$C$点$\frac{16}{5}$.
|
|
|
|
023142
|
|
$\frac{\sqrt{39}}{2}$.
|
|
|
|
016740
|
|
1.
|
|
|
|
016731
|
|
8.
|
|
|
|
023143
|
|
$\arctan\frac{1}{5}$或者$\arctan\frac{4}{5}$.
|
|
|
|
023144
|
|
$\arctan\frac{2\sqrt{5}}{5}$.
|
|
|
|
017767
|
|
2
|
|
|
|
023145
|
|
$\sqrt{6}$.
|
|
|
|
023146
|
|
$\frac{\sqrt{3}}{3}$.
|
|
|
|
023147
|
|
$[ 30,90 ]$.
|
|
|
|
023148
|
|
(1) $\frac{\sqrt{15}}{5}$; (2) $\frac{\pi}{6}$.
|
|
|
|
023149
|
|
$\frac{\sqrt{3}}{2}$.
|
|
|
|
023150
|
|
$\frac{2}{3}$.
|
|
|
|
023151
|
|
(1) $\arctan \frac{\sqrt{5}}{5}$; (2) $\arccos \frac{\sqrt{30}}{10}$; (3) 在 $BC$ 边上存在一点 $G$, $BG$的值为1.
|
|
|
|
023152
|
|
(1) 略; (2) $\arcsin \frac{\sqrt{21}}{7}$; (3) 存在 $P$, 使得 $DE \parallel $ 平面 $BMP$, $\dfrac{AP}{DP}$ 的值3.
|
|
|
|
031552
|
|
$\frac{\sqrt{10}}{5}$
|
|
|
|
003489
|
|
(1) $\arcsin \frac{\sqrt{6}}{3}$; (2) $\arcsin \frac{\sqrt{3}}{3}$; (3) $\frac{\pi}{4}$.
|
|
|
|
023153
|
|
(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{\sqrt{6}}{6}$; (3) $\frac{\sqrt{6}}{6}$.
|
|
|
|
003456
|
|
$\frac{3\sqrt{5}}{5}$.
|
|
|
|
003457
|
|
$\frac{\pi}{3}$或$\frac{2\pi}{3}$.
|
|
|
|
023154
|
|
1或3.
|
|
|
|
023155
|
|
$\frac{\pi}{3}$.
|
|
|
|
023156
|
|
\textcircled{1}\textcircled{2}\textcircled{3}\textcircled{5}.
|
|
|
|
023157
|
|
B
|
|
|
|
023158
|
|
B
|
|
|
|
023159
|
|
A
|
|
|
|
023160
|
|
$\frac{\pi}{3}$.
|
|
|
|
023161
|
|
4.3
|
|
|
|
023162
|
|
(1) 略; (2) $\frac{\sqrt{3}}{2}$; (3) $\arcsin \frac{2\sqrt{5}}{5}$.
|
|
|
|
023163
|
|
(1) $\frac{\pi}{2}$; (2) $\frac{\pi}{3}$.
|
|
|
|
023164
|
|
(1) 四边形 $MNDC$为矩形; (2) $\arctan \frac{\sqrt{2}}{2}$; (3) $\frac{\sqrt{2}}{2}$.
|
|
|
|
023165
|
|
(1) 异面直线 $D_1E$ 与 $A_1D$ 所成角的大小不会随点 $E$ 的移动而改变, 所成角为$\frac{\pi}{2}$; \\(2) 点 $E$距离点 $A$ 为$2-\sqrt{3}$, 二面角 $D_1-EC-D$ 的大小为 $\dfrac{\pi}{4}$; \\(3) 直线 $AD_1$ 平行于 平面 $B_1DE$.
|
|
|
|
023166
|
|
\textcircled{2}\textcircled{3}
|
|
|
|
023167
|
|
$75^{\circ}$
|
|
|
|
010502
|
|
arctan$\frac{\sqrt{5}}{5}$
|
|
|
|
023168
|
|
arccos$\frac{2}{3}$
|
|
|
|
023169
|
|
$\frac{\pi}{4}$
|
|
|
|
023170
|
|
$\sqrt{41}$或$13$
|
|
|
|
023171
|
|
$6$或$1.5$
|
|
|
|
023172
|
|
$30^{\circ}$
|
|
|
|
023173
|
|
$3.5cm$
|
|
|
|
023174
|
|
$\frac{\sqrt{2}}{2}$
|
|
|
|
023175
|
|
B
|
|
|
|
023176
|
|
$A$
|
|
|
|
023177
|
|
$D$
|
|
|
|
023178
|
|
$(1)$略; $(2)\frac{\sqrt{14}}{14}$
|
|
|
|
023179
|
|
$(1)\frac{\pi}{6};(2)arccos\frac{\sqrt{3}}{3}$
|
|
|
|
023180
|
|
$(1)$略; $(2)arctan\frac{\sqrt{6}}{2}$;$(3)$略; $(4)\frac{\sqrt{2}}{6}$
|
|
|
|
023181
|
|
无
|
|
|
|
011402
|
|
A
|
|
|
|
023182
|
|
B.
|
|
|
|
023183
|
|
2.
|
|
|
|
023184
|
|
5.
|
|
|
|
023185
|
|
$\sqrt{29}$.
|
|
|
|
023186
|
|
$\frac{\pi}{6}$.
|
|
|
|
023187
|
|
$\frac{15\sqrt{3}}{2}$
|
|
|
|
017677
|
|
$DM\perp PC$(或$BM\perp PC$)
|
|
|
|
023188
|
|
\textcircled{1}\textcircled{2}\textcircled{4}
|
|
|
|
023189
|
|
(1)略; (2)$arccos\frac{\sqrt{15}}{5}$
|
|
|
|
023190
|
|
(1)略; (2)6.
|
|
|
|
023191
|
|
$S=\begin{cases}\frac{1}{2cos\alpha},\quad\alpha\in(0,arctan\sqrt{2}]\\ \frac{\sqrt{2}-cot\alpha}{sin\alpha},\alpha\in(arctan\sqrt{2},\frac{\pi}{2}]\end{cases}$
|
|
|
|
023192
|
|
(1)略; (2)$\frac{2\sqrt{6}}{3}$.
|
|
|
|
023193
|
|
$8$.
|
|
|
|
023194
|
|
$arctan\frac{\sqrt{3}}{2}$.
|
|
|
|
023195
|
|
$64.$
|
|
|
|
023196
|
|
$arctan\sqrt{2}$.
|
|
|
|
023197
|
|
$10.$
|
|
|
|
023198
|
|
$(1)$外心; $(2)$内心; $(3)$垂心.
|
|
|
|
023199
|
|
$\sqrt{3}$
|
|
|
|
023200
|
|
$48$.
|
|
|
|
023201
|
|
$\frac{6}{7}$.
|
|
|
|
023202
|
|
A.
|
|
|
|
023203
|
|
$S=32,V=16$.
|
|
|
|
023204
|
|
$\frac{2\sqrt{11}}{11}$.
|
|
|
|
023205
|
|
$(1)$略; $(2)\frac{5}{3}$.
|
|
|
|
023206
|
|
$(1)V=a^2;(2)$\textcircled{1}$\frac{\sqrt{51}}{9}$;\textcircled{2}$\frac{\sqrt{30}}{3}$.
|
|
|
|
023207
|
|
$\sqrt{29}$.
|
|
|
|
023208
|
|
$\frac{\sqrt{6}}{3}$.
|
|
|
|
023209
|
|
$arctan\frac{\sqrt{5}}{5}$.
|
|
|
|
023210
|
|
$arccos\frac{2}{3}$.
|
|
|
|
023211
|
|
$\frac{\pi}{6}$.
|
|
|
|
023212
|
|
$\frac{15\sqrt{3}}{2}$.
|
|
|
|
023213
|
|
$3\pi^2$或$\frac{9}{2}\pi^2$.
|
|
|
|
023214
|
|
$\frac{\sqrt{3}}{2}a$.
|
|
|
|
023215
|
|
$\pi$.
|
|
|
|
023216
|
|
$\sqrt{2}:1$.
|
|
|
|
023217
|
|
$1:4:9$.
|
|
|
|
023218
|
|
$\frac{8}{3}\pi$.
|
|
|
|
023219
|
|
$12:15:20$.
|
|
|
|
023220
|
|
$576$.
|
|
|
|
023221
|
|
$\theta_{min}=\pi-arctan\frac{4}{3}$,此时$P$ 在线段 $A_1C_1$ 的中点.
|
|
|
|
023222
|
|
略.
|
|
|
|
023223
|
|
$(1)$略; $(2)arctan\sqrt{2}$;$(3)$是, $\frac{\sqrt{6}}{24}$.
|
|
|
|
023224
|
|
$P^{6}_{20-m}$.
|
|
|
|
023225
|
|
$60$.
|
|
|
|
023226
|
|
$48$.
|
|
|
|
023227
|
|
$6$.
|
|
|
|
023228
|
|
$6$.
|
|
|
|
023229
|
|
$156$.
|
|
|
|
023230
|
|
$103$.
|
|
|
|
023231
|
|
$48$.
|
|
|
|
023232
|
|
$(\frac{2}{3},1)$.
|
|
|
|
023233
|
|
$a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
|
|
\end{cases}$.
|
|
|
|
023234
|
|
(1)$m=9$;(2)$k_{n}=3^{n+1}+2$.
|
|
|
|
023235
|
|
$(-\frac{1}{11},-\frac{1}{19})$.
|
|
|
|
023236
|
|
(1)略; (2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$.
|
|
|
|
023237
|
|
$1716$.
|
|
|
|
023238
|
|
5或8.
|
|
|
|
023239
|
|
$x=15,y=5$.
|
|
|
|
023240
|
|
21.
|
|
|
|
023241
|
|
6.
|
|
|
|
016908
|
|
12.
|
|
|
|
023242
|
|
540.
|
|
|
|
023243
|
|
2880.
|
|
|
|
023244
|
|
200.
|
|
|
|
023245
|
|
$-1$.
|
|
|
|
023246
|
|
$2^{n-1},n\in \mathbf{N}$且$n\ge1$.
|
|
|
|
023247
|
|
$2^{n-1},n\in \mathbf{N}$且$n\ge1$.
|
|
|
|
023248
|
|
$7(\frac{1}{3})^{n-1}-6,n\in \mathbf{N}$且$n\ge1$.
|
|
|
|
023249
|
|
$765$.
|
|
|
|
023250
|
|
(1)58409520;(2)6275430;(3)64684945;(4)64682995.
|
|
|
|
023251
|
|
$92$.
|
|
|
|
023256
|
|
$\frac{3}{5}$
|
|
|
|
023257
|
|
$\frac{3}{7}$
|
|
|
|
023258
|
|
$\frac{1}{35}$
|
|
|
|
031430
|
|
$\frac{14}{33}$
|
|
|
|
017716
|
|
$\frac{3}{10}$
|
|
|
|
017041
|
|
$\frac{3}{4}$
|
|
|
|
023259
|
|
$\frac{2}{7}$
|
|
|
|
023260
|
|
$\frac{2}{27}$
|
|
|
|
023261
|
|
$\frac{9}{10}$
|
|
|
|
023262
|
|
$-49$
|
|
|
|
023263
|
|
$12$
|
|
|
|
023264
|
|
$\frac{5}{6}$
|
|
|
|
023265
|
|
(1) $d_1, d_2, d_3$ 的值分别为2,3,6;\\
|
|
(2) 略; (3) 略.
|
|
|
|
023266
|
|
$0.54$
|
|
|
|
023267
|
|
$\dfrac{5}{36}$; $\dfrac{5}{12}$
|
|
|
|
023268
|
|
$\dfrac{3}{8}$; $\dfrac{7}{8}$
|
|
|
|
023269
|
|
$0.88$
|
|
|
|
023270
|
|
$0.9$
|
|
|
|
023271
|
|
$7$或$8$
|
|
|
|
002651
|
|
$7$
|
|
|
|
023272
|
|
(1) F; (2) F; (3) T; (4) F.
|
|
|
|
023273
|
|
(1) $\dfrac{4}{15}$; (2) $\dfrac{11}{15}$
|
|
|
|
023274
|
|
(1) $\dfrac{70}{323}$; (2) $\dfrac{728}{969}$; (3) $\dfrac{27}{128}$
|
|
|
|
023275
|
|
(1) $\dfrac{211}{3456}$; (2) $\dfrac{7}{10}$; (3) $\dfrac{1}{15}$
|
|
|
|
023276
|
|
(1) $c_n=2n-1$; (2) $S_n=1+(n-1)3^n$
|
|
|
|
023277
|
|
$18$
|
|
|
|
023278
|
|
B
|
|
|
|
023279
|
|
A
|
|
|
|
023280
|
|
C
|
|
|
|
023281
|
|
B
|
|
|
|
023282
|
|
C
|
|
|
|
023283
|
|
$55$
|
|
|
|
023284
|
|
$50$; $1015$
|
|
|
|
023285
|
|
$3$
|
|
|
|
023286
|
|
$n=1$时, $a_n=5$; $n \geq 2$时, $a_n=2n-2$
|
|
|
|
023287
|
|
$2^n+3$
|
|
|
|
023288
|
|
$1049410$
|
|
|
|
023289
|
|
$19$
|
|
|
|
023290
|
|
(1) $0.5$; (2) $\frac{3}{16}$; (3) 略
|
|
|
|
023291
|
|
(1) $\{a_n\}-3n+15$; (2) $T_n=\frac{1}{6}(\frac{3}{2}-\frac{1}{n+1}-\frac{1}{n+2})$
|
|
|
|
023292
|
|
(1) $P_3=-2p^3+3p^2$; $P_4=4p^3-3p^4$; (2) 当$0<p<\frac{1}{2}$时,做一道且及格的概率最大; 当$p=\frac{1}{2}$时,做一道或者三道且及格的概率最大; 当$\frac{1}{2}<p<1$时,做三道且及格的概率最大.
|
|
|
|
023294
|
|
(1) 略; (2) $\sqrt{2}$
|
|
|
|
023295
|
|
(1) $\frac{2}{3}$; 在 $BC$ 边上存在一点 $G$, 使得点 $D$ 到平面 $PAG$ 的距离为 $\sqrt{2}$, $|BG|=1$; (3) $|HB|=\frac{\sqrt{5}}{3}$.
|
|
|
|
023296
|
|
A
|
|
|
|
023297
|
|
B
|
|
|
|
023298
|
|
C
|
|
|
|
023299
|
|
D
|
|
|
|
023300
|
|
C
|
|
|
|
023301
|
|
C
|
|
|
|
023302
|
|
$0.325$; $81.5$
|
|
|
|
017209
|
|
$0.98$
|
|
|
|
023303
|
|
4; $\sqrt{3}$
|
|
|
|
023304
|
|
$1$
|
|
|
|
023305
|
|
(1) $0.04$; (2) $440$.
|
|
|
|
023306
|
|
\textcircled{1}\textcircled{4}
|
|
|
|
023307
|
|
$100$ 名观众的样本平均数和方差分别约为$19.9$ 和$15.1$, 估计所有观众新闻类节目收看时长的总体方差约为$15.1$.
|
|
|
|
023308
|
|
(2) 二级; (3) $4400$
|
|
|
|
023309
|
|
$36\pi$
|
|
|
|
023285
|
|
$3$
|
|
|
|
023310
|
|
$[\frac{\pi}{3},\frac{\pi}{2}]$
|
|
|
|
023311
|
|
$3$
|
|
|
|
023312
|
|
$\frac{\sqrt{2}a}{2}$
|
|
|
|
023313
|
|
C
|
|
|
|
023314
|
|
B
|
|
|
|
023315
|
|
(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{3\sqrt{2}}{2}$; (3) $\frac{\sqrt{6}}{3}$
|
|
|
|
023316
|
|
$1047.2$立方厘米
|
|
|
|
023317
|
|
(1) $S_n=2^n-1$; (2) $T_n=2^{n+1}-2-n$
|
|
|
|
023318
|
|
$10$
|
|
|
|
023319
|
|
$\frac{2}{5}$
|
|
|
|
023320
|
|
$19$
|
|
|
|
023321
|
|
$\dfrac{6}{\pi}$
|
|
|
|
023322
|
|
$84$
|
|
|
|
023323
|
|
$480$
|
|
|
|
023324
|
|
$a$
|
|
|
|
023325
|
|
$2\pi$
|
|
|
|
023326
|
|
$2$
|
|
|
|
023327
|
|
$\frac{33}{40}$
|
|
|
|
023328
|
|
$2$
|
|
|
|
023329
|
|
$1440$
|
|
|
|
023330
|
|
$\frac{8}{15}$
|
|
|
|
023331
|
|
$6\sqrt{3}$
|
|
|
|
023332
|
|
$8:27$
|
|
|
|
023333
|
|
$27$
|
|
|
|
014424
|
|
$13$
|
|
|
|
023334
|
|
$28$
|
|
|
|
023335
|
|
$\frac{5}{12}$
|
|
|
|
023336
|
|
$56-\frac{40\pi}{3}$
|
|
|
|
023337
|
|
$64$
|
|
|
|
023338
|
|
$\frac{\sqrt{3}}{4}$
|
|
|
|
023339
|
|
D
|
|
|
|
023340
|
|
A
|
|
|
|
023341
|
|
B
|
|
|
|
023342
|
|
C
|
|
|
|
023343
|
|
C
|
|
|
|
023344
|
|
D
|
|
|
|
023345
|
|
(1) $\frac{2}{3}$; (2) $\frac{1}{6}$
|
|
|
|
023346
|
|
(1) $-32$; (2) $-17$; (3) $-5$
|
|
|
|
023347
|
|
(1) $a, b$ 的值分别为$0.005,0.025$; (2) 估计这个 100 名候选者面试成绩的平均数和第 60 百分位数分别约为$69.5$和$71.7$; (3) $\frac{3}{5}$.
|
|
|
|
023348
|
|
(1) $\arccos \frac{1}{3}$; (2) $4\sqrt{3}+2$
|
|
|
|
023349
|
|
(1) $\{b_n\}=n-(-1)^n \cdot n^2$;
|
|
(2) \textcircled{1} $T_{10}=0$; \textcircled{2} $2575$
|
|
|
|
023350
|
|
$2352$
|
|
|
|
023351
|
|
$25 \times 2^{100}$
|
|
|
|
023352
|
|
$18$
|
|
|
|
023353
|
|
C
|
|
|
|
023354
|
|
$2\sqrt{3}$
|
|
|
|
023355
|
|
$\frac{85}{256}$
|
|
|
|
|
|
ans
|
|
|
|
022801
|
|
$[0,1]$
|
|
|
|
022802
|
|
$\sqrt{5}$
|
|
|
|
022803
|
|
$2\sqrt{2}-1$
|
|
|
|
022804
|
|
$\pm 1$
|
|
|
|
022805
|
|
$2n-3$
|
|
|
|
022806
|
|
$1$
|
|
|
|
022807
|
|
$36$
|
|
|
|
012041
|
|
$240$
|
|
|
|
022808
|
|
若 \textcircled{1}\textcircled{3},则\textcircled{2}(或者若 \textcircled{2}\textcircled{3},则\textcircled{1})
|
|
|
|
012042
|
|
$(-1,1)$
|
|
|
|
022809
|
|
$\dfrac{4\sqrt{3}}{3}$
|
|
|
|
022810
|
|
A
|
|
|
|
022811
|
|
D
|
|
|
|
022812
|
|
A
|
|
|
|
022813
|
|
$(1)\dfrac{\pi}{4});(2)4-\sqrt{2}$
|
|
|
|
022814
|
|
(1)$\dfrac{\pi}{3}$;(2)$\arctan\dfrac{\sqrt{2}}{2}$;(3)$\dfrac{1}{2}$
|
|
|
|
004486
|
|
(1) 约为$6.7^\circ$; (2) 最小值为$256$
|
|
|
|
022815
|
|
(1) $\dfrac{x^2}{2}+y^2=1$; (2) $k=\pm\dfrac{1}{2}$
|
|
|
|
022816
|
|
(1) $\dfrac{1}{1},\dfrac{2}{1},\dfrac{1}{2},\dfrac{3}{1},\dfrac{2}{2},\dfrac{1}{3},\dfrac{4}{1},\dfrac{3}{2},\dfrac{2}{3},\dfrac{1}{4}$; (2) $1008\dfrac{28}{65}$
|
|
|
|
019810
|
|
$\{2,4\}$
|
|
|
|
019811
|
|
$x=\log_23$
|
|
|
|
031267
|
|
$4\pi$
|
|
|
|
012389
|
|
$n^2$
|
|
|
|
019814
|
|
$2$
|
|
|
|
019815
|
|
$\dfrac{\pi}{6}$
|
|
|
|
009322
|
|
$72$
|
|
|
|
019817
|
|
$\dfrac{2\sqrt{2}}{3}$
|
|
|
|
019818
|
|
$\dfrac{3}{10}$
|
|
|
|
019819
|
|
$-3$
|
|
|
|
040079
|
|
$1078$
|
|
|
|
019822
|
|
B
|
|
|
|
019823
|
|
A
|
|
|
|
004565
|
|
B
|
|
|
|
022817
|
|
(1) $\arctan\dfrac{2}{5}$; (2) $V=4$
|
|
|
|
022818
|
|
(1) $a=0$; (2) $a-\dfrac{1}{4}$
|
|
|
|
022819
|
|
(1)7小时; (2)17小时
|
|
|
|
022820
|
|
(1)$4\sqrt{2}-6$;(2)$y=-\dfrac{\sqrt{2}}{2}x$
|
|
|
|
022821
|
|
(1) $1,2,3,a_n=n$;(2)略
|
|
|
|
022822
|
|
$\sqrt{2}$
|
|
|
|
022823
|
|
3
|
|
|
|
022824
|
|
$1+\ln x$
|
|
|
|
022825
|
|
$\sqrt{5}\pi$
|
|
|
|
022826
|
|
0
|
|
|
|
022827
|
|
80
|
|
|
|
022828
|
|
$-\dfrac{1}{4}$
|
|
|
|
022829
|
|
$\dfrac{y^2}{9}-\dfrac{x^2}{1}=1$
|
|
|
|
022830
|
|
$\dfrac{9}{20}$
|
|
|
|
022831
|
|
8
|
|
|
|
022832
|
|
$\dfrac{\sqrt{5}}{2}$
|
|
|
|
022833
|
|
D
|
|
|
|
022834
|
|
A
|
|
|
|
022835
|
|
C
|
|
|
|
022836
|
|
(1) $\dfrac{16}{3}$;(2) $\arcsin\dfrac{2\sqrt{2}}{3}$
|
|
|
|
004506
|
|
(1) $1$;(2)$2$
|
|
|
|
022837
|
|
(1)$3.1$秒; (2)20米/秒, 72千米/小时
|
|
|
|
022838
|
|
(1)$\dfrac{8}{3}$;(2)略
|
|
|
|
022839
|
|
(1)$a_1=1;a_2=0$或$1$; $a_3=0$或$1$;(2)115,证明略
|
|
|
|
022840
|
|
$\{1,2\}$
|
|
|
|
022841
|
|
$\dfrac{\pi}{3}$
|
|
|
|
022842
|
|
$\dfrac{\pi}{3}$
|
|
|
|
022843
|
|
$-2$
|
|
|
|
022844
|
|
$512$
|
|
|
|
022845
|
|
$\dfrac{2\pi}{3}$
|
|
|
|
022846
|
|
$-3$
|
|
|
|
022847
|
|
$\dfrac{x^2}{9}-\dfrac{y^2}{16}=1$
|
|
|
|
022848
|
|
$(0,\dfrac{1}{3})\bigcup (\dfrac{1}{3},\dfrac{2}{3})$
|
|
|
|
022849
|
|
$2:-1:1:1$
|
|
|
|
022850
|
|
$\dfrac{\sqrt{3}}{2}$
|
|
|
|
022851
|
|
C
|
|
|
|
022852
|
|
C
|
|
|
|
022853
|
|
A
|
|
|
|
022854
|
|
(1)12;(2)略
|
|
|
|
022855
|
|
(1)$AB=\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$1$平方米; (2)$AB=2\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$2$平方米
|
|
|
|
022856
|
|
(1)$2020$;(2)$(-\infty,\log_2\dfrac{9}{10}]$
|
|
|
|
022857
|
|
(1)证明略; (2)关于直线$y=x$对称, $x$范围为$[-1,+\infty)$,$y$范围为$[-1,+\infty)$,证明略
|
|
|
|
022858
|
|
(1)例: $f(x)=\sin\dfrac{\pi x}{4}$,证明略; (2)证明略
|
|
|
|
022859
|
|
$(0,2)$
|
|
|
|
004512
|
|
$\sqrt{2}$
|
|
|
|
022860
|
|
$(x+\dfrac{3}{2})^2+y^2=9$
|
|
|
|
022861
|
|
$2n+1$
|
|
|
|
004558
|
|
$15$
|
|
|
|
019885
|
|
$2\pi$
|
|
|
|
022862
|
|
$0.25$
|
|
|
|
022863
|
|
$3\sqrt{3}$
|
|
|
|
022864
|
|
$[0,\dfrac{\sqrt{3}}{3}]$
|
|
|
|
004521
|
|
$(-\infty,-1]$
|
|
|
|
022865
|
|
A
|
|
|
|
022866
|
|
A
|
|
|
|
004524
|
|
C
|
|
|
|
022867
|
|
(1)证明略; (2)$ED=\dfrac{\sqrt{6}}{3}a$
|
|
|
|
004527
|
|
(1)$T=\pi $;严格增区间为$[k\pi-\dfrac{\pi}{3},k\pi+\dfrac{\pi}{6}],k\in\mathbf{Z}$;(2)$3\sqrt{3}$
|
|
|
|
022868
|
|
(1)15户; (2)$x=5$时, $f(x)$最大值为$2.12>2.1$,可以达到
|
|
|
|
022869
|
|
(1)$1$; (2)$(0,\arctan\dfrac{1}{2})$
|
|
|
|
022870
|
|
(1)$6$; (2)正确, 证明略 |