高一数学题 高一数学题(函数)?

\u9ad8\u4e00\u6570\u5b66\u7ec3\u4e60\u9898

\u4e00\u3001\u9009\u62e9\u9898

1\uff0e\u4e0b\u5217\u516b\u4e2a\u5173\u7cfb\u5f0f\u2460{0}= \u2461 =0 \u2462 { } \u2463 { } \u2464{0} \u24650 \u2466 {0} \u2467 { }\u5176\u4e2d\u6b63\u786e\u7684\u4e2a\u6570\uff08 \uff09
\uff08A\uff094 \uff08B\uff095 \uff08C\uff096 \uff08D\uff097
2\uff0e\u96c6\u5408{1\uff0c2\uff0c3}\u7684\u771f\u5b50\u96c6\u5171\u6709\uff08 \uff09
\uff08A\uff095\u4e2a \uff08B\uff096\u4e2a \uff08C\uff097\u4e2a \uff08D\uff098\u4e2a
3\uff0e\u96c6\u5408A={x } B={ } C={ }\u53c8 \u5219\u6709\uff08 \uff09
\uff08A\uff09\uff08a+b\uff09 A (B) (a+b) B (C)(a+b) C (D) (a+b) A\u3001B\u3001C\u4efb\u4e00\u4e2a
4\uff0e\u8bbeA\u3001B\u662f\u5168\u96c6U\u7684\u4e24\u4e2a\u5b50\u96c6\uff0c\u4e14A B\uff0c\u5219\u4e0b\u5217\u5f0f\u5b50\u6210\u7acb\u7684\u662f\uff08 \uff09
\uff08A\uff09CUA CUB \uff08B\uff09CUA CUB=U
\uff08C\uff09A CUB= \uff08D\uff09CUA B=
5\uff0e\u5df2\u77e5\u96c6\u5408A={ } B={ }\u5219A =\uff08 \uff09
\uff08A\uff09R \uff08B\uff09{ }
\uff08C\uff09{ } \uff08D\uff09{ }
6\uff0e\u4e0b\u5217\u8bed\u53e5\uff1a\uff081\uff090\u4e0e{0}\u8868\u793a\u540c\u4e00\u4e2a\u96c6\u5408\uff1b\uff082\uff09\u75311\uff0c2\uff0c3\u7ec4\u6210\u7684\u96c6\u5408\u53ef\u8868\u793a\u4e3a{1\uff0c2\uff0c3}\u6216{3\uff0c2\uff0c1}\uff1b\uff083\uff09\u65b9\u7a0b\uff08x-1\uff092(x-2)2=0\u7684\u6240\u6709\u89e3\u7684\u96c6\u5408\u53ef\u8868\u793a\u4e3a{1\uff0c1\uff0c2}\uff1b\uff084\uff09\u96c6\u5408{ }\u662f\u6709\u9650\u96c6\uff0c\u6b63\u786e\u7684\u662f\uff08 \uff09
\uff08A\uff09\u53ea\u6709\uff081\uff09\u548c\uff084\uff09 \uff08B\uff09\u53ea\u6709\uff082\uff09\u548c\uff083\uff09
\uff08C\uff09\u53ea\u6709\uff082\uff09 \uff08D\uff09\u4ee5\u4e0a\u8bed\u53e5\u90fd\u4e0d\u5bf9
7\uff0e\u5df2\u77e5A={1\uff0c2\uff0ca2-3a-1},B={1,3},A {3,1}\u5219a\u7b49\u4e8e\uff08 \uff09
\uff08A\uff09-4\u62161 \uff08B\uff09-1\u62164 \uff08C\uff09-1 \uff08D\uff094
8.\u8bbeU={0\uff0c1\uff0c2\uff0c3\uff0c4}\uff0cA={0\uff0c1\uff0c2\uff0c3}\uff0cB={2\uff0c3\uff0c4}\uff0c\u5219\uff08CUA\uff09 \uff08CUB\uff09=\uff08 \uff09
\uff08A\uff09{0} \uff08B\uff09{0\uff0c1}
\uff08C\uff09{0\uff0c1\uff0c4} \uff08D\uff09{0\uff0c1\uff0c2\uff0c3\uff0c4}
9\uff0e\u8bbeS\u3001T\u662f\u4e24\u4e2a\u975e\u7a7a\u96c6\u5408\uff0c\u4e14S T\uff0cT S\uff0c\u4ee4X=S \u90a3\u4e48S X=\uff08 \uff09
\uff08A\uff09X \uff08B\uff09T \uff08C\uff09 \uff08D\uff09S
10\uff0e\u8bbeA={x },B={x },\u82e5A B={2,3,5},A\u3001B\u5206\u522b\u4e3a\uff08 \uff09
\uff08A\uff09{3\uff0c5}\u3001{2\uff0c3} \uff08B\uff09{2\uff0c3}\u3001{3\uff0c5}
\uff08C\uff09{2\uff0c5}\u3001{3\uff0c5} \uff08D\uff09{3\uff0c5}\u3001{2\uff0c5}
11\uff0e\u8bbe\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0bax2+bx+c=0(a<0)\u7684\u6839\u7684\u5224\u522b\u5f0f \uff0c\u5219\u4e0d\u7b49\u5f0fax2+bx+c 0\u7684\u89e3\u96c6\u4e3a\uff08 \uff09
\uff08A\uff09R \uff08B\uff09
\uff08C\uff09{ } \uff08D\uff09{ }
\uff08A\uff09P Q
\uff08B\uff09Q P
\uff08C\uff09P=Q \uff08D\uff09P Q=
12\uff0e\u5df2\u77e5P={ }\uff0cQ={ \uff0c\u5bf9\u4e8e\u4e00\u5207 R\u6210\u7acb}\uff0c\u5219\u4e0b\u5217\u5173\u7cfb\u5f0f\u4e2d\u6210\u7acb\u7684\u662f\uff08 \uff09

13\uff0e\u82e5M={ }\uff0cN={ Z}\uff0c\u5219M N\u7b49\u4e8e\uff08 \uff09
\uff08A\uff09 \uff08B\uff09{ } \uff08C\uff09{0} \uff08D\uff09Z
14\uff0e\u4e0b\u5217\u5404\u5f0f\u4e2d\uff0c\u6b63\u786e\u7684\u662f\uff08 \uff09
\uff08A\uff092
\uff08B\uff09{ }
\uff08C\uff09{ }
\uff08D\uff09{ }={ }
15\uff0e\u8bbeU={1\uff0c2\uff0c3\uff0c4\uff0c5}\uff0cA\uff0cB\u4e3aU\u7684\u5b50\u96c6\uff0c\u82e5A B={2}\uff0c\uff08CUA\uff09 B={4}\uff0c\uff08CUA\uff09 \uff08CUB\uff09={1\uff0c5}\uff0c\u5219\u4e0b\u5217\u7ed3\u8bba\u6b63\u786e\u7684\u662f\uff08 \uff09
\uff08A\uff093 \uff08B\uff093
\uff08C\uff093 \uff08D\uff093
16\uff0e\u82e5U\u3001 \u5206\u522b\u8868\u793a\u5168\u96c6\u548c\u7a7a\u96c6\uff0c\u4e14\uff08CUA\uff09 A\uff0c\u5219\u96c6\u5408A\u4e0eB\u5fc5\u987b\u6ee1\u8db3\uff08 \uff09
(A) (B)
(C)B= (D)A=U\u4e14A B
17\uff0e\u5df2\u77e5U=N\uff0cA={ }\uff0c\u5219CUA\u7b49\u4e8e\uff08 \uff09
\uff08A\uff09{0\uff0c1\uff0c2\uff0c3\uff0c4\uff0c5\uff0c6} \uff08B\uff09{1\uff0c2\uff0c3\uff0c4\uff0c5\uff0c6}
\uff08C\uff09{0\uff0c1\uff0c2\uff0c3\uff0c4\uff0c5} \uff08D\uff09{1\uff0c2\uff0c3\uff0c4\uff0c5}
18\uff0e\u4e8c\u6b21\u51fd\u6570y=-3x2+mx+m+1\u7684\u56fe\u50cf\u4e0ex\u8f74\u6ca1\u6709\u4ea4\u70b9\uff0c\u5219m\u7684\u53d6\u503c\u8303\u56f4\u662f\uff08 \uff09
\uff08A\uff09{ } \uff08B\uff09{ }
\uff08C\uff09{ } \uff08D\uff09{ }
19\uff0e\u8bbe\u5168\u96c6U={\uff08x,y\uff09 },\u96c6\u5408M={\uff08x,y\uff09 }\uff0cN={(x,y) },\u90a3\u4e48\uff08CUM\uff09 \uff08CUN\uff09\u7b49\u4e8e\uff08 \uff09
\uff08A\uff09{\uff082\uff0c-2\uff09} \uff08B\uff09{\uff08-2\uff0c2\uff09}
\uff08C\uff09 \uff08D\uff09\uff08CUN\uff09
20\uff0e\u4e0d\u7b49\u5f0f <x2-4\u7684\u89e3\u96c6\u662f\uff08 \uff09
\uff08A\uff09{x } \uff08B\uff09{x }
\uff08C\uff09{ x } \uff08D\uff09{ x }
\u4e8c\u3001\u586b\u7a7a\u9898
1\uff0e \u5728\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0c\u5750\u6807\u8f74\u4e0a\u7684\u70b9\u7684\u96c6\u5408\u53ef\u8868\u793a\u4e3a
2\uff0e \u82e5A={1,4,x},B={1,x2}\u4e14A B=B\uff0c\u5219x=
3\uff0e \u82e5A={x } B={x },\u5168\u96c6U=R\uff0c\u5219A =
4\uff0e \u82e5\u65b9\u7a0b8x2+(k+1)x+k-7=0\u6709\u4e24\u4e2a\u8d1f\u6839\uff0c\u5219k\u7684\u53d6\u503c\u8303\u56f4\u662f
5\uff0e \u96c6\u5408{a,b,c}\u7684\u6240\u6709\u5b50\u96c6\u662f \u771f\u5b50\u96c6\u662f \uff1b\u975e\u7a7a\u771f\u5b50\u96c6\u662f
6\uff0e \u65b9\u7a0bx2-5x+6=0\u7684\u89e3\u96c6\u53ef\u8868\u793a\u4e3a
\u65b9\u7a0b\u7ec4
7\uff0e\u8bbe\u96c6\u5408A={ },B={x },\u4e14A B\uff0c\u5219\u5b9e\u6570k\u7684\u53d6\u503c\u8303\u56f4\u662f
\u3002
8\uff0e\u8bbe\u5168\u96c6U={x \u4e3a\u5c0f\u4e8e20\u7684\u975e\u8d1f\u5947\u6570}\uff0c\u82e5A \uff08CUB\uff09={3\uff0c7\uff0c15}\uff0c\uff08CUA\uff09 B={13\uff0c17\uff0c19}\uff0c\u53c8\uff08CUA\uff09 \uff08CUB\uff09= \uff0c\u5219A B=
9\uff0e\u8bbeU={\u4e09\u89d2\u5f62}\uff0cM={\u76f4\u89d2\u4e09\u89d2\u5f62}\uff0cN={\u7b49\u8170\u4e09\u89d2\u5f62}\uff0c\u5219M N=
M N= CUM=
CUN= CU\uff08M N\uff09=
10\uff0e\u8bbe\u5168\u96c6\u4e3a \uff0c\u7528\u96c6\u5408A\u3001B\u3001C\u7684\u4ea4\u3001\u5e76\u3001\u8865\u96c6\u7b26\u53f7\u8868\u56fe\u4e2d\u7684\u9634\u5f71\u90e8\u5206\u3002
\uff081\uff09 \uff082\uff09
\uff083\uff09
\u4e09\u3001\u89e3\u7b54\u9898
1\uff0e\u8bbe\u5168\u96c6U={1\uff0c2\uff0c3\uff0c4}\uff0c\u4e14={ x2-5x+m=0,x U}\u82e5CUA={1\uff0c4}\uff0c\u6c42m\u7684\u503c\u3002



2\uff0e\u5df2\u77e5\u96c6\u5408A={a \u5173\u4e8ex\u7684\u65b9\u7a0bx2-ax+1=0,\u6709\u5b9e\u6839}\uff0cB={a \u4e0d\u7b49\u5f0fax2-x+1>0\u5bf9\u4e00\u5207x R\u6210\u7acb},\u6c42A B\u3002



3\uff0e\u5df2\u77e5\u96c6\u5408A={a2,a+1,-3},B={a-3,2a-1,a2+1}, \u82e5A B={-3}\uff0c\u6c42\u5b9e\u6570a\u3002



4\uff0e\u5df2\u77e5\u65b9\u7a0bx2-(k2-9)+k2-5k+6=0\u7684\u4e00\u6839\u5c0f\u4e8e1\uff0c\u53e6\u4e00\u6839\u5927\u4e8e2\uff0c\u6c42\u5b9e\u6570k\u7684\u53d6\u503c\u8303\u56f4\u3002



5\uff0e\u8bbeA={x ,\u5176\u4e2dx R,\u5982\u679cA B=B\uff0c\u6c42\u5b9e\u6570a\u7684\u53d6\u503c\u8303\u56f4\u3002




6\uff0e\u8bbe\u5168\u96c6U={x },\u96c6\u5408A={x },B={ x2+px+12=0},\u4e14\uff08CUA\uff09 B={1\uff0c4\uff0c3\uff0c5}\uff0c\u6c42\u5b9e\u6570P\u3001q\u7684\u503c\u3002

7\uff0e\u82e5\u4e0d\u7b49\u5f0fx2-ax+b0\u7684\u89e3\u96c6\u3002



8\uff0e\u96c6\u5408A={\uff08x,y\uff09 },\u96c6\u5408B={\uff08x,y\uff09 ,\u4e140 }\uff0c\u53c8A \uff0c\u6c42\u5b9e\u6570m\u7684\u53d6\u503c\u8303\u56f4\u3002


\u7b2c\u4e00\u5355\u5143 \u96c6\u5408
\u4e00\u3001 \u9009\u62e9\u9898
\u9898\u53f7 1 2 3 4 5 6 7 8 9 10
\u7b54\u6848 B C B C B C B C D A
\u9898\u53f7 11 12 13 14 15 16 17 18 19 20
\u7b54\u6848 D A A D C D A D A B
\u4e8c\u3001 \u586b\u7a7a\u9898\u7b54\u6848
1\uff0e{(x,y) } 2.0, 3.{x ,\u6216x 3} 4.{ } 5. ,{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c};\u9664\u53bb{a,b,c}\u5916\u6240\u6709\u5b50\u96c6\uff1b\u9664\u53bb \u53ca{a,b,c}\u5916\u7684\u6240\u6709\u5b50\u96c6 6.{2,3};{2,3} 7.{ } 8.{1,5,9,11} 9.{\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62}\uff1b{\u7b49\u8170\u6216\u76f4\u89d2\u4e09\u89d2\u5f62}\uff0c{\u659c\u4e09\u89d2\u5f62}\uff0c{\u4e0d\u7b49\u8fb9\u4e09\u89d2\u5f62}\uff0c{\u65e2\u975e\u7b49\u8170\u4e5f\u975e\u76f4\u89d2\u4e09\u89d2\u5f62}\u3002 10.\uff081\uff09 \uff08A B\uff09 \uff082\uff09[\uff08CUA\uff09 \uff08CUB\uff09] \uff1b\uff083\uff09\uff08A B\uff09 \uff08CUC\uff09
\u4e09\u3001\u89e3\u7b54\u9898
1\uff0em=2\u00d73=6 2.{a } 3.a=-1
4. \u63d0\u793a\uff1a\u4ee4f(1)<0 \u4e14f(2)<0\u89e3\u5f97
5\uff0e\u63d0\u793a\uff1aA={0\uff0c-4}\uff0c\u53c8A B=B\uff0c\u6240\u4ee5B A
\uff08\u2160\uff09B= \u65f6\uff0c 4\uff08a+1\uff092-4(a2-1)<0\uff0c\u5f97a<-1
(\u2161)B={0}\u6216B={-4}\u65f6\uff0c 0 \u5f97a=-1
\uff08\u2162\uff09B={0\uff0c-4}\uff0c \u89e3\u5f97a=1
\u7efc\u4e0a\u6240\u8ff0\u5b9e\u6570a=1 \u6216a -1
6\uff0eU={1\uff0c2\uff0c3\uff0c4\uff0c5} A={1\uff0c4}\u6216A={2\uff0c3} CuA={2,3,5}\u6216{1\uff0c4\uff0c5} B={3\uff0c4}\uff08CUA\uff09 B=\uff081\uff0c3\uff0c4\uff0c5\uff09\uff0c\u53c8 B={3\uff0c4} CUA={1\uff0c4\uff0c5} \u6545A\u53ea\u6709\u7b49\u4e8e\u96c6\u5408{2\uff0c3}
P=-\uff083+4\uff09=-7 q=2\u00d73=6
7\uff0e\u65b9\u7a0bx2-ax-b=0\u7684\u89e3\u96c6\u4e3a{2\uff0c3}\uff0c\u7531\u97e6\u8fbe\u5b9a\u7406a=2+3=5,b=2\u00d73=6,\u4e0d\u7b49\u5f0fbx2-ax+1>0\u5316\u4e3a6x2-5x+1>0 \u89e3\u5f97{x }
8.\u7531A B \u77e5\u65b9\u7a0b\u7ec4
\u5f97x2+(m-1)x=0 \u57280 x \u5185\u6709\u89e3\uff0c \u5373m 3\u6216m -1\u3002
\u82e5 3\uff0c\u5219x1+x2=1-m<0,x1x2=1,\u6240\u4ee5\u65b9\u7a0b\u53ea\u6709\u8d1f\u6839\u3002
\u82e5m -1,x1+x2=1-m>0,x1x2=1,\u6240\u4ee5\u65b9\u7a0b\u6709\u4e24\u6b63\u6839\uff0c\u4e14\u4e24\u6839\u5747\u4e3a1\u6216\u4e24\u6839\u4e00\u4e2a\u5927\u4e8e1\uff0c\u4e00\u4e2a\u5c0f\u4e8e1\uff0c\u5373\u81f3\u5c11\u6709\u4e00\u6839\u5728[0\uff0c2]\u5185\u3002
\u56e0\u6b64{m <m -1}\u3002

\u5982\u56fe:


\u5982\u679c\u6ee1\u610f\u8bf7\u91c7\u7eb3\u6216\u8005\u70b9\u8d5e\uff0c\u8c22\u8c22

f(x)=(sinx+cosx)²-2cos²x-m 在x∈[0,π]上有两个零点x1,x2 求tan(x1+x2)

令f(x)=(sinx+cosx)²-2cos²x-m =0,方程的解就是函数的零点。

分离变量:m=(sinx+cosx)²-2cos²x  x∈[0,π]

转化为函数y=m与函数y=(sinx+cosx)²-2cos²x图像在x∈[0,π]上有两个交点,交点的横坐标即为x1,x2

y=(sinx+cosx)²-2cos²x

=1+2sinxcosx--2cos²x (用二倍角公式)

=sin2x-cos2x  (用辅助角公式)

=√2sin(2x-π/4)

对称轴为2x-π/4=π/2+2kπ

x=3π/8+kπ

2x-π/4∈[-π/4,3π/4]  所以 sin(2x-π/4)∈[-√2/2,1]  

所以1<m≤√2

(x1+x2)/2=3π/8

x1+x2=3π/4

tan(x1+x2)不存在=tan(3π/4)=-1。




供参考。



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