diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt index feb69cb3..e0a54c86 100644 --- a/工具v2/文本文件/metadata.txt +++ b/工具v2/文本文件/metadata.txt @@ -1,1825 +1,4 @@ -ans +remark -018366 -(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) $x=k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$ - -018367 -(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) $\{x|x=\dfrac{k\pi}{2}+\dfrac{\pi}{4}, \ k\in \mathbf{Z}\}$ - -018369 -(1) $x=-\dfrac{\pi}{2}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{\pi}{6}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$ - -009563 -(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) $\{x|x=\dfrac{k\pi}{3}+\dfrac{\pi}{6}, \ k\in \mathbf{Z}\}$ - -018372 -$\dfrac{\sqrt{6}-\sqrt{2}}{4}$, $\dfrac{\sqrt{6}+\sqrt{2}}{4}$ - -018373 -$-\dfrac{56}{65}$ - -018375 -$\dfrac{\pi}{3}$ - -009564 -(1) $\dfrac{\sqrt{2}}{2}$; (2) $\dfrac{\sqrt{3}}{2}$ - -009565 -$-\dfrac{7\sqrt{2}}{26}$ - -018377 -(1) $\dfrac{\sqrt{3}}{2}$; (2) $\cos 2\alpha$; (3) $-\cos 3x$ - -018376 -$-\dfrac{4}{5}$ - -018378 -$\dfrac{\sqrt{6}-\sqrt{2}}{4}$ - -018379 -证明略 - -018380 -(1) $-1$; (2) $\dfrac{1}{7}$ - -018381 -$-\sqrt{3}$ - -009567 -(1) $\dfrac{\sqrt{3}}{2}$; (2) $\sqrt{3}$ - -009568 -$\dfrac{\sqrt{2}}{10}$, $7$ - -009569 -(1) 证明略; (2) 证明略 - -018385 -证明略 - -018386 -$(-\dfrac{\sqrt{2}}{2},\dfrac{3\sqrt{2}}{2})$ - -018387 -(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$\cos\varphi=\dfrac{a}{\sqrt{a^2+b^2}}$, $\sin\varphi=\dfrac{b}{\sqrt{a^2+b^2}}$ - -024614 -$\{\alpha|\alpha=2k\pi\text{或}\dfrac{2\pi}{3}+2k\pi, \ k\in \mathbf{Z}\}$ - -009570 -$\sin C=\dfrac{220}{221}$, $\cos C=-\dfrac{21}{221}$ - -009571 -$\sin(\alpha+\beta)=\dfrac{33}{65}$, $\cos(\alpha+\beta)=-\dfrac{56}{65}$, $\alpha+\beta$是第二象限角 - -009572 -(1) $\sqrt{2}\sin(\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha+\dfrac{2\pi}{3})$ - -018390 -$\dfrac{\sqrt{6}-\sqrt{2}}{4}$ - -018402 -证明略 - -018403 -证明略 - -018404 -证明略 - -009576 -证明略 - -009577 -证明略 - -009578 -证明略 - -018405 -证明略 - -040387 -$\dfrac{5\pi}{3}$ - -040388 -$-1$ - -040389 -$-\dfrac{\pi}{3}$或$\dfrac{4\pi}{3}$ - -040390 -$-3$ - -040391 -$-2$ - -040392 -$-\dfrac{\sqrt{23}}{4}$ - -ans - -041050 -$2\sqrt{7}$, $(0,\pm \sqrt{7})$ - -040971 -$2\sqrt{7}$, $(\pm \sqrt{7},0)$ - -041051 -D - -040972 -$x=0(-3 \leq y \leq 3)$ - -040973 -B - -040974 -$\dfrac{x^2}7+\dfrac{y^2}{16}=1$ - -040975 -B - -008878 -D - -008877 -A - -014470 -$4\sqrt{3}$ - -040976 -$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}7+\dfrac{y^2}{16}=1$ - -040977 -(1)$\dfrac{x^2}{100}+\dfrac{y^2}{64}=1$; -(2)$\dfrac{x^2}6+\dfrac{y^2}4=1$ - -040978 -(1)$k=7$;(2)$4\sqrt{3}$ - -040995 -(1)$y=-\sqrt12+\sqrt34$;(2)$x+4y=0$(点在已知椭圆内);(3)$x^2+x+2y^2=0$ - -040996 -$6\sqrt{5}$ - -021204 -$\dfrac{\sqrt{2}}{2}$ - -021205 -$2\sqrt{37}$,$2$ - -021206 -$\dfrac{x^2}{25}+\dfrac{y^2}{75}=1$ - -021207 -$\dfrac{x^2}{12}+\dfrac{y^2}{9}=1$或$\dfrac{x^2}{9}+\dfrac{y^2}{12}=1$ - -021208 -$[-\sqrt{34},\sqrt{34}]$ - -021209 -$\dfrac{\pi}3$ - -040997 -$b\sqrt{a^2-b^2}$ - -040998 -$8\sqrt{3}$ - -021212 -$P(-6,-4)$,$d=\dfrac{22}{\sqrt{73}}$ - -021200 -$\dfrac{x^2}{4}+y^2=1$ - -021201 -$-\dfrac{5\sqrt{7}}{4}0)$;(3)$x^2-\dfrac{y^2}{3}=1$ - -021223 -$\dfrac{x^2}{20}-\dfrac{y^2}{16}=1$ - -021224 -$\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$ - -021225 -不正确, 正确结果为$17$ - -021226 -$\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$ - -021227 -D - -021228 -$(-3,6)$ - -021229 -$m<-2$ - -021230 -$\dfrac{41}{4}$ - -021231 -$32+2m$ - -021232 -$|PF_1|=\dfrac{c}{a}x_0+a$,$|PF_2|=\dfrac{c}{a}x_0-a$ - -021233 -$x^2-\dfrac{y^2}{4}=1$ - -041001 -(1)$\dfrac{y^2}{18}-\dfrac{x^2}{18}=1$,$\sqrt{2}$;(2)$(\pm 2\sqrt{3},0)$,$\arctan{2\sqrt{2}}$ - -041002 -A,A,B,B - -041003 -(1))$\dfrac{x^2}{3}-\dfrac{y^2}{5}=1$;(2))$\dfrac{y^2}{81}-\dfrac{x^2}{9}=1$或)$x^2-\dfrac{y^2}{9}=1$ - -021242 -$\dfrac{x^2}{3}-\dfrac{y^2}{12}=1$ - -021243 -$y=\pm \dfrac{\sqrt{2}}{4}x$ - -021244 -证明略 - -041004 -(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)$(\pm \sqrt{7},0)$ - -041005 -D,A,D - -021251 -$a^2$ - -021263 -$\dfrac{y^2}{36}-\dfrac{x^2}{81}=1(x\neq 0)$ - -021252 -$\dfrac{c}{a}$ - -021253 -$y=\pm \sqrt{2}x$ - -021254 -$0$ - -008917 -$\dfrac{x^2}{4}-\dfrac{y^2}{5}=1$(x>0) - -021255 -$\dfrac{2\sqrt{3}}{3}$ - -021256 -$\dfrac{14\sqrt{3}}{3}$ - -041006 -$3$ - -021258 -$x^2-4y^2=\pm \dfrac{36}{5}$ - -021259 -$(-\dfrac{\sqrt{15}}{3},-1)$ - -021260 -(1)椭圆:$k<4$,双曲线: $4\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$ - -ans - -012360 -$\dfrac{\pi}{3}$ - -009305 -(1)$x^15$,$-15x^14$,$105x^13$,$-455x^12$\\ -(2)$-2099520a^9b^14$ - -009306 -(1)$\dfrac{105}{8}$;(2)$-252$ - -009309 -$120$ - -009308 -证明略 - -009317 -(1)第$18$,$19$项; \\ -(2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$ - -009319 -证明略 - -021093 -(1)$\dfrac{1}{45}$;(2)$\dfrac{7}{10}$ - -022919 -(1)$\dfrac{1}{36}$;(2)$\dfrac{1}{18}$;(3)$\dfrac{5}{12}$ - -021095 -(1)$\dfrac{1}{68880}$;(2)$\dfrac{1}{11480}$ - -021096 -$\dfrac37$ - -021097 -$\dfrac{1}{12}$ - -021098 -$\dfrac{18}{25}$ - -021099 -$\dfrac{2}{5}$ - -021101 -$\dfrac{11}{12}$ - -021102 -$\dfrac{3439}{10000}$ - -021103 -$\dfrac{n!}{n^n}$ - -021104 -$\dfrac{1}{15}$ - -021105 -$\dfrac15$ - -021106 -(1)$\dfrac{11}{42}$;(2)$\dfrac{31}{42}$ - -021107 -(1)$\dfrac{1279}{1785}$;(2)$\dfrac{59049}{139075300}$ - -021108 -(1)$\{5,7,9\}$;(2)$\{0,2,4,5,6,7,8,9\}$;(3)$\emptyset$ - -021109 -B - -021110 -(1)$\{1,2,3,4\}$;(2)A - -021111 -(1)$\{1,2,3,4\}$;(2)A - -021112 -充分非必要 - -021113 -(1)$A\cup B$;(2)$A \cap \overline{B}$;(3)$(A \cap \overline{B}) \cup(\overline{A} \cap B) $ - -021114 -$B\subseteq \overline{A}$,$\overline{A}\cup \overline{B}=\omega$ - -021116 -(1)$\dfrac12$;(2)$\dfrac56$;(3)$\dfrac23$;(4)$\dfrac56$ - -021117 -(1)不是;(2)$0.94$ - -021125 -(1)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)\cup (A \cap B \cap C)$; -(2)$\overline{A\cap B \cap C }$; -(3)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)$ - -021118 -$\dfrac47$,$\dfrac27$,$\dfrac17$,$\dfrac67$,$\dfrac67$,$\dfrac57$ - -019932 -(1)$\dfrac34$;(2)$\dfrac1{13}$;(3)$\dfrac12$;(4)$\dfrac{51}{52}$ - -021119 -$\dfrac45$ - -021120 -$\dfrac35$ - -021121 -$\dfrac14$,$\dfrac16$,$\dfrac14$ - -021122 -$0.9$,$0.1$ - -018762 -证明略 - -021126 -大数定律 - -021127 -$\dfrac{73}{75}$ - -021128 -$\dfrac34$,$\dfrac{9}{44}$,$\dfrac{9}{220}$.$\dfrac{1}{220}$ - -021129 -(1)$0.46$;(2)$0.51$;(3)$0.97$ - -021130 -(1)$0.852$;(2)$25560$;(3)$5869$ - -021131 -(1)$0.1,0.06,0.025,0.02,0.02,0.02$;(2)$0.02$;(3)$40$ - -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$02.1$,可以达到 - -022869 -(1)$1$; (2)$(0,\arctan\dfrac{1}{2})$ - -022870 -(1)$6$; (2)正确, 证明略 \ No newline at end of file +18412 +批改时注意学生应有判断并舍去钝角的过程 diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 73183500..a38e960a 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -507359,7 +507359,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "\\\\\n批改时注意学生应有判断并舍去钝角的过程", "space": "4em", "unrelated": [] },