课代表罚我抄数学高中必修5所有公式10犯法没? 高中数学必修1~5所有公式
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\u5e0c\u671b\u5bf9\u4f60\u6709\u5e2e\u52a9\uff1a
.
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\u3000\u524dn\u9879\u548c\u516c\u5f0f\u4e3a\uff1aSn=na1+n(n-1)d/2
\u3000\u3000Sn=(a1+an)n/2 \u3000
\u3000\u82e5m+n=p+q\u5219\uff1a\u5b58\u5728am+an=ap+aq \u3000
\u3000\u82e5m+n=2p\u5219\uff1aam+an=2ap
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\u82e5\u901a\u9879\u516c\u5f0f\u53d8\u5f62\u4e3aan=a1/q*q^n(n\u2208N*),\u5f53q\uff1e0\u65f6\uff0c
\u5219\u53ef\u628aan\u770b\u4f5c\u81ea\u53d8\u91cfn\u7684\u51fd\u6570\uff0c\u70b9(n,an)\u662f\u66f2\u7ebfy=a1/q*q^x\u4e0a\u7684\u4e00\u7fa4\u5b64\u7acb\u7684\u70b9\u3002 \u3000
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(5) \u7b49\u6bd4\u6c42\u548c\uff1aSn=a1+a2+a3+.......+an \u3000
\u2460\u5f53q\u22601\u65f6\uff0cSn=a1(1-q^n)/(1-q)\u6216Sn=(a1-an\u00d7q)\u00f7(1-q) \u3000\u3000\u2461\u5f53q=1\u65f6\uff0c Sn=n\u00d7a1\uff08q=1\uff09 \u3000
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1\u3001\u96c6\u5408\u7684\u542b\u4e49\uff1a\u67d0\u4e9b\u6307\u5b9a\u7684\u5bf9\u8c61\u96c6\u5728\u4e00\u8d77\u5c31\u6210\u4e3a\u4e00\u4e2a\u96c6\u5408\uff0c\u5176\u4e2d\u6bcf\u4e00\u4e2a\u5bf9\u8c61\u53eb\u5143\u7d20\u3002
2\u3001\u96c6\u5408\u7684\u4e2d\u5143\u7d20\u7684\u4e09\u4e2a\u7279\u6027\uff1a
1.\u5143\u7d20\u7684\u786e\u5b9a\u6027\uff1b 2.\u5143\u7d20\u7684\u4e92\u5f02\u6027\uff1b 3.\u5143\u7d20\u7684\u65e0\u5e8f\u6027
\u8bf4\u660e\uff1a(1)\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u96c6\u5408\uff0c\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u662f\u786e\u5b9a\u7684\uff0c\u4efb\u4f55\u4e00\u4e2a\u5bf9\u8c61\u6216\u8005\u662f\u6216\u8005\u4e0d\u662f\u8fd9\u4e2a\u7ed9\u5b9a\u7684\u96c6\u5408\u7684\u5143\u7d20\u3002
(2)\u4efb\u4f55\u4e00\u4e2a\u7ed9\u5b9a\u7684\u96c6\u5408\u4e2d\uff0c\u4efb\u4f55\u4e24\u4e2a\u5143\u7d20\u90fd\u662f\u4e0d\u540c\u7684\u5bf9\u8c61\uff0c\u76f8\u540c\u7684\u5bf9\u8c61\u5f52\u5165\u4e00\u4e2a\u96c6\u5408\u65f6\uff0c\u4ec5\u7b97\u4e00\u4e2a\u5143\u7d20\u3002
(3)\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u662f\u5e73\u7b49\u7684\uff0c\u6ca1\u6709\u5148\u540e\u987a\u5e8f\uff0c\u56e0\u6b64\u5224\u5b9a\u4e24\u4e2a\u96c6\u5408\u662f\u5426\u4e00\u6837\uff0c\u4ec5\u9700\u6bd4\u8f83\u5b83\u4eec\u7684\u5143\u7d20\u662f\u5426\u4e00\u6837\uff0c\u4e0d\u9700\u8003\u67e5\u6392\u5217\u987a\u5e8f\u662f\u5426\u4e00\u6837\u3002
(4)\u96c6\u5408\u5143\u7d20\u7684\u4e09\u4e2a\u7279\u6027\u4f7f\u96c6\u5408\u672c\u8eab\u5177\u6709\u4e86\u786e\u5b9a\u6027\u548c\u6574\u4f53\u6027\u3002
3\u3001\u96c6\u5408\u7684\u8868\u793a\uff1a{ \u2026 } \u5982{\u6211\u6821\u7684\u7bee\u7403\u961f\u5458}\uff0c{\u592a\u5e73\u6d0b,\u5927\u897f\u6d0b,\u5370\u5ea6\u6d0b,\u5317\u51b0\u6d0b}
1. \u7528\u62c9\u4e01\u5b57\u6bcd\u8868\u793a\u96c6\u5408\uff1aA={\u6211\u6821\u7684\u7bee\u7403\u961f\u5458},B={1,2,3,4,5}
2\uff0e\u96c6\u5408\u7684\u8868\u793a\u65b9\u6cd5\uff1a\u5217\u4e3e\u6cd5\u4e0e\u63cf\u8ff0\u6cd5\u3002
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\u6b63\u6574\u6570\u96c6 N*\u6216 N+ \u6574\u6570\u96c6Z \u6709\u7406\u6570\u96c6Q \u5b9e\u6570\u96c6R
\u5173\u4e8e\u201c\u5c5e\u4e8e\u201d\u7684\u6982\u5ff5
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4\u3001\u96c6\u5408\u7684\u5206\u7c7b\uff1a
1\uff0e\u6709\u9650\u96c6 \u542b\u6709\u6709\u9650\u4e2a\u5143\u7d20\u7684\u96c6\u5408
2\uff0e\u65e0\u9650\u96c6 \u542b\u6709\u65e0\u9650\u4e2a\u5143\u7d20\u7684\u96c6\u5408
3\uff0e\u7a7a\u96c6 \u4e0d\u542b\u4efb\u4f55\u5143\u7d20\u7684\u96c6\u5408 \u4f8b\uff1a{x|x2=\uff0d5\uff5d \u4e8c\u3001\u96c6\u5408\u95f4\u7684\u57fa\u672c\u5173\u7cfb 1.\u201c\u5305\u542b\u201d\u5173\u7cfb\u2014\u5b50\u96c6 \u6ce8\u610f\uff1a \u6709\u4e24\u79cd\u53ef\u80fd\uff081\uff09A\u662fB\u7684\u4e00\u90e8\u5206\uff0c\uff1b\uff082\uff09A\u4e0eB\u662f\u540c\u4e00\u96c6\u5408\u3002 \u53cd\u4e4b: \u96c6\u5408A\u4e0d\u5305\u542b\u4e8e\u96c6\u5408B,\u6216\u96c6\u5408B\u4e0d\u5305\u542b\u96c6\u5408A,\u8bb0\u4f5cA B\u6216B A 2\uff0e\u201c\u76f8\u7b49\u201d\u5173\u7cfb(5\u22655\uff0c\u4e145\u22645\uff0c\u52195=5) \u5b9e\u4f8b\uff1a\u8bbe A={x|x2-1=0} B={-1,1} \u201c\u5143\u7d20\u76f8\u540c\u201d
\u7ed3\u8bba\uff1a\u5bf9\u4e8e\u4e24\u4e2a\u96c6\u5408A\u4e0eB\uff0c\u5982\u679c\u96c6\u5408A\u7684\u4efb\u4f55\u4e00\u4e2a\u5143\u7d20\u90fd\u662f\u96c6\u5408B\u7684\u5143\u7d20\uff0c\u540c\u65f6,\u96c6\u5408B\u7684\u4efb\u4f55\u4e00\u4e2a\u5143\u7d20\u90fd\u662f\u96c6\u5408A\u7684\u5143\u7d20\uff0c\u6211\u4eec\u5c31\u8bf4\u96c6\u5408A\u7b49\u4e8e\u96c6\u5408B\uff0c\u5373\uff1aA=B
\u2460 \u4efb\u4f55\u4e00\u4e2a\u96c6\u5408\u662f\u5b83\u672c\u8eab\u7684\u5b50\u96c6\u3002A�8�2A
\u2461\u771f\u5b50\u96c6:\u5982\u679cA�8�2B,\u4e14A�8�2 B\u90a3\u5c31\u8bf4\u96c6\u5408A\u662f\u96c6\u5408B\u7684\u771f\u5b50\u96c6\uff0c\u8bb0\u4f5cA B(\u6216B A)
\u2462\u5982\u679c A�8�2B, B�8�2C ,\u90a3\u4e48 A�8�2C
\u2463 \u5982\u679cA�8�2B \u540c\u65f6 B�8�2A \u90a3\u4e48A=B
3. \u4e0d\u542b\u4efb\u4f55\u5143\u7d20\u7684\u96c6\u5408\u53eb\u505a\u7a7a\u96c6\uff0c\u8bb0\u4e3a\u03a6
\u89c4\u5b9a: \u7a7a\u96c6\u662f\u4efb\u4f55\u96c6\u5408\u7684\u5b50\u96c6\uff0c \u7a7a\u96c6\u662f\u4efb\u4f55\u975e\u7a7a\u96c6\u5408\u7684\u771f\u5b50\u96c6\u3002
\u4e09\u3001\u96c6\u5408\u7684\u8fd0\u7b97
1\uff0e\u4ea4\u96c6\u7684\u5b9a\u4e49\uff1a\u4e00\u822c\u5730\uff0c\u7531\u6240\u6709\u5c5e\u4e8eA\u4e14\u5c5e\u4e8eB\u7684\u5143\u7d20\u6240\u7ec4\u6210\u7684\u96c6\u5408,\u53eb\u505aA,B\u7684\u4ea4\u96c6\uff0e
\u8bb0\u4f5cA\u2229B(\u8bfb\u4f5c\u201dA\u4ea4B\u201d)\uff0c\u5373A\u2229B={x|x\u2208A\uff0c\u4e14x\u2208B}\uff0e
2\u3001\u5e76\u96c6\u7684\u5b9a\u4e49\uff1a\u4e00\u822c\u5730\uff0c\u7531\u6240\u6709\u5c5e\u4e8e\u96c6\u5408A\u6216\u5c5e\u4e8e\u96c6\u5408B\u7684\u5143\u7d20\u6240\u7ec4\u6210\u7684\u96c6\u5408\uff0c\u53eb\u505aA,B\u7684\u5e76\u96c6\u3002\u8bb0\u4f5c\uff1aA\u222aB(\u8bfb\u4f5c\u201dA\u5e76B\u201d)\uff0c\u5373A\u222aB={x|x\u2208A\uff0c\u6216x\u2208B}\uff0e
3\u3001\u4ea4\u96c6\u4e0e\u5e76\u96c6\u7684\u6027\u8d28\uff1aA\u2229A = A, A\u2229\u03c6= \u03c6, A\u2229B = B\u2229A\uff0cA\u222aA = A,
A\u222a\u03c6= A ,A\u222aB = B\u222aA.
4\u3001\u5168\u96c6\u4e0e\u8865\u96c6
\uff081\uff09\u8865\u96c6\uff1a\u8bbeS\u662f\u4e00\u4e2a\u96c6\u5408\uff0cA\u662fS\u7684\u4e00\u4e2a\u5b50\u96c6\uff08\u5373 \uff09\uff0c\u7531S\u4e2d\u6240\u6709\u4e0d\u5c5e\u4e8eA\u7684\u5143\u7d20\u7ec4\u6210\u7684\u96c6\u5408\uff0c\u53eb\u505aS\u4e2d\u5b50\u96c6A\u7684\u8865\u96c6\uff08\u6216\u4f59\u96c6\uff09
\u8bb0\u4f5c\uff1a CSA \u5373 CSA ={x �8�1 x�8�3S\u4e14 x�8�4A}
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\uff083\uff09\u6027\u8d28\uff1a\u2474CU(C UA)=A \u2475(C UA)\u2229A=\u03a6 \u2476(CUA)\u222aA=U
\u4e8c\u3001\u51fd\u6570\u7684\u6709\u5173\u6982\u5ff5
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(\u89c1\u8bfe\u672c21\u9875\u76f8\u5173\u4f8b2)
\u503c\u57df\u8865\u5145
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\u4f8b\u5982: y=2sinX y=2cos(X2+1)
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\u5982\u679c\u5bf9\u4e8e\u533a\u95f4D\u4e0a\u7684\u4efb\u610f\u4e24\u4e2a\u81ea\u53d8\u91cf\u7684\u503cx1\uff0cx2\uff0c\u5f53x1<x2 \u65f6\uff0c\u90fd\u6709f(x1)\uff1ef(x2)\uff0c\u90a3\u4e48\u5c31\u8bf4f(x)\u5728\u8fd9\u4e2a\u533a\u95f4\u4e0a\u662f\u51cf\u51fd\u6570.\u533a\u95f4D\u79f0\u4e3ay=f(x)\u7684\u5355\u8c03\u51cf\u533a\u95f4.
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\u25cb2 \u5fc5\u987b\u662f\u5bf9\u4e8e\u533a\u95f4D\u5185\u7684\u4efb\u610f\u4e24\u4e2a\u81ea\u53d8\u91cfx1\uff0cx2\uff1b\u5f53x1<x2\u65f6\uff0c\u603b\u6709f(x1)<f(x2) \u3002
\uff082\uff09 \u56fe\u8c61\u7684\u7279\u70b9
\u5982\u679c\u51fd\u6570y=f(x)\u5728\u67d0\u4e2a\u533a\u95f4\u662f\u589e\u51fd\u6570\u6216\u51cf\u51fd\u6570\uff0c\u90a3\u4e48\u8bf4\u51fd\u6570y=f(x)\u5728\u8fd9\u4e00\u533a\u95f4\u4e0a\u5177\u6709(\u4e25\u683c\u7684)\u5355\u8c03\u6027\uff0c\u5728\u5355\u8c03\u533a\u95f4\u4e0a\u589e\u51fd\u6570\u7684\u56fe\u8c61\u4ece\u5de6\u5230\u53f3\u662f\u4e0a\u5347\u7684\uff0c\u51cf\u51fd\u6570\u7684\u56fe\u8c61\u4ece\u5de6\u5230\u53f3\u662f\u4e0b\u964d\u7684.
(3).\u51fd\u6570\u5355\u8c03\u533a\u95f4\u4e0e\u5355\u8c03\u6027\u7684\u5224\u5b9a\u65b9\u6cd5
(A) \u5b9a\u4e49\u6cd5\uff1a
\u25cb1 \u4efb\u53d6x1\uff0cx2\u2208D\uff0c\u4e14x1<x2\uff1b\u25cb2 \u4f5c\u5deef(x1)\uff0df(x2)\uff1b\u25cb3 \u53d8\u5f62\uff08\u901a\u5e38\u662f\u56e0\u5f0f\u5206\u89e3\u548c\u914d\u65b9\uff09\uff1b\u25cb4 \u5b9a\u53f7\uff08\u5373\u5224\u65ad\u5deef(x1)\uff0df(x2)\u7684\u6b63\u8d1f\uff09\uff1b\u25cb5 \u4e0b\u7ed3\u8bba\uff08\u6307\u51fa\u51fd\u6570f(x)\u5728\u7ed9\u5b9a\u7684\u533a\u95f4D\u4e0a\u7684\u5355\u8c03\u6027\uff09\uff0e
(B)\u56fe\u8c61\u6cd5(\u4ece\u56fe\u8c61\u4e0a\u770b\u5347\u964d)_
(C)\u590d\u5408\u51fd\u6570\u7684\u5355\u8c03\u6027
\u590d\u5408\u51fd\u6570f[g(x)]\u7684\u5355\u8c03\u6027\u4e0e\u6784\u6210\u5b83\u7684\u51fd\u6570u=g(x)\uff0cy=f(u)\u7684\u5355\u8c03\u6027\u5bc6\u5207\u76f8\u5173\uff0c\u5176\u89c4\u5f8b\u5982\u4e0b\uff1a
\u51fd\u6570 \u5355\u8c03\u6027
u=g(x) \u589e \u589e \u51cf \u51cf
y=f(u) \u589e \u51cf \u589e \u51cf
y=f[g(x)] \u589e \u51cf \u51cf \u589e
\u6ce8\u610f\uff1a1\u3001\u51fd\u6570\u7684\u5355\u8c03\u533a\u95f4\u53ea\u80fd\u662f\u5176\u5b9a\u4e49\u57df\u7684\u5b50\u533a\u95f4 ,\u4e0d\u80fd\u628a\u5355\u8c03\u6027\u76f8\u540c\u7684\u533a\u95f4\u548c\u5728\u4e00\u8d77\u5199\u6210\u5176\u5e76\u96c6. 2\u3001\u8fd8\u8bb0\u5f97\u6211\u4eec\u5728\u9009\u4fee\u91cc\u5b66\u4e60\u7b80\u5355\u6613\u884c\u7684\u5bfc\u6570\u6cd5\u5224\u5b9a\u5355\u8c03\u6027\u5417\uff1f
8\uff0e\u51fd\u6570\u7684\u5947\u5076\u6027
\uff081\uff09\u5076\u51fd\u6570
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\uff082\uff09\uff0e\u5947\u51fd\u6570
\u4e00\u822c\u5730\uff0c\u5bf9\u4e8e\u51fd\u6570f(x)\u7684\u5b9a\u4e49\u57df\u5185\u7684\u4efb\u610f\u4e00\u4e2ax\uff0c\u90fd\u6709f(\uff0dx)=\u2014f(x)\uff0c\u90a3\u4e48f(x)\u5c31\u53eb\u505a\u5947\u51fd\u6570\uff0e
\u6ce8\u610f\uff1a\u25cb1 \u51fd\u6570\u662f\u5947\u51fd\u6570\u6216\u662f\u5076\u51fd\u6570\u79f0\u4e3a\u51fd\u6570\u7684\u5947\u5076\u6027\uff0c\u51fd\u6570\u7684\u5947\u5076\u6027\u662f\u51fd\u6570\u7684\u6574\u4f53\u6027\u8d28\uff1b\u51fd\u6570\u53ef\u80fd\u6ca1\u6709\u5947\u5076\u6027,\u4e5f\u53ef\u80fd\u65e2\u662f\u5947\u51fd\u6570\u53c8\u662f\u5076\u51fd\u6570\u3002
\u25cb2 \u7531\u51fd\u6570\u7684\u5947\u5076\u6027\u5b9a\u4e49\u53ef\u77e5\uff0c\u51fd\u6570\u5177\u6709\u5947\u5076\u6027\u7684\u4e00\u4e2a\u5fc5\u8981\u6761\u4ef6\u662f\uff0c\u5bf9\u4e8e\u5b9a\u4e49\u57df\u5185\u7684\u4efb\u610f\u4e00\u4e2ax\uff0c\u5219\uff0dx\u4e5f\u4e00\u5b9a\u662f\u5b9a\u4e49\u57df\u5185\u7684\u4e00\u4e2a\u81ea\u53d8\u91cf\uff08\u5373\u5b9a\u4e49\u57df\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff09\uff0e
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\u5076\u51fd\u6570\u7684\u56fe\u8c61\u5173\u4e8ey\u8f74\u5bf9\u79f0\uff1b\u5947\u51fd\u6570\u7684\u56fe\u8c61\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff0e
\u603b\u7ed3\uff1a\u5229\u7528\u5b9a\u4e49\u5224\u65ad\u51fd\u6570\u5947\u5076\u6027\u7684\u683c\u5f0f\u6b65\u9aa4\uff1a\u25cb1 \u9996\u5148\u786e\u5b9a\u51fd\u6570\u7684\u5b9a\u4e49\u57df\uff0c\u5e76\u5224\u65ad\u5176\u5b9a\u4e49\u57df\u662f\u5426\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff1b\u25cb2 \u786e\u5b9af(\uff0dx)\u4e0ef(x)\u7684\u5173\u7cfb\uff1b\u25cb3 \u4f5c\u51fa\u76f8\u5e94\u7ed3\u8bba\uff1a\u82e5f(\uff0dx) = f(x) \u6216 f(\uff0dx)\uff0df(x) = 0\uff0c\u5219f(x)\u662f\u5076\u51fd\u6570\uff1b\u82e5f(\uff0dx) =\uff0df(x) \u6216 f(\uff0dx)\uff0bf(x) = 0\uff0c\u5219f(x)\u662f\u5947\u51fd\u6570\uff0e
\u6ce8\u610f\u554a\uff1a\u51fd\u6570\u5b9a\u4e49\u57df\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\u662f\u51fd\u6570\u5177\u6709\u5947\u5076\u6027\u7684\u5fc5\u8981\u6761\u4ef6\uff0e\u9996\u5148\u770b\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u662f\u5426\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff0c\u82e5\u4e0d\u5bf9\u79f0\u5219\u51fd\u6570\u662f\u975e\u5947\u975e\u5076\u51fd\u6570.\u82e5\u5bf9\u79f0\uff0c(1)\u518d\u6839\u636e\u5b9a\u4e49\u5224\u5b9a; (2)\u6709\u65f6\u5224\u5b9af(-x)=\u00b1f(x)\u6bd4\u8f83\u56f0\u96be\uff0c\u53ef\u8003\u8651\u6839\u636e\u662f\u5426\u6709f(-x)\u00b1f(x)=0\u6216f(x)/f(-x)=\u00b11\u6765\u5224\u5b9a; (3)\u5229\u7528\u5b9a\u7406\uff0c\u6216\u501f\u52a9\u51fd\u6570\u7684\u56fe\u8c61\u5224\u5b9a .
9\u3001\u51fd\u6570\u7684\u89e3\u6790\u8868\u8fbe\u5f0f
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10\uff0e\u51fd\u6570\u6700\u5927\uff08\u5c0f\uff09\u503c\uff08\u5b9a\u4e49\u89c1\u8bfe\u672cp36\u9875\uff09
\u25cb1 \u5229\u7528\u4e8c\u6b21\u51fd\u6570\u7684\u6027\u8d28\uff08\u914d\u65b9\u6cd5\uff09\u6c42\u51fd\u6570\u7684\u6700\u5927\uff08\u5c0f\uff09\u503c\u25cb2 \u5229\u7528\u56fe\u8c61\u6c42\u51fd\u6570\u7684\u6700\u5927\uff08\u5c0f\uff09\u503c\u25cb3 \u5229\u7528\u51fd\u6570\u5355\u8c03\u6027\u7684\u5224\u65ad\u51fd\u6570\u7684\u6700\u5927\uff08\u5c0f\uff09\u503c\uff1a\u5982\u679c\u51fd\u6570y=f(x)\u5728\u533a\u95f4[a\uff0cb]\u4e0a\u5355\u8c03\u9012\u589e\uff0c\u5728\u533a\u95f4[b\uff0cc]\u4e0a\u5355\u8c03\u9012\u51cf\u5219\u51fd\u6570y=f(x)\u5728x=b\u5904\u6709\u6700\u5927\u503cf(b)\uff1b\u5982\u679c\u51fd\u6570y=f(x)\u5728\u533a\u95f4[a\uff0cb]\u4e0a\u5355\u8c03\u9012\u51cf\uff0c\u5728\u533a\u95f4[b\uff0cc]\u4e0a\u5355\u8c03\u9012\u589e\u5219\u51fd\u6570y=f(x)\u5728x=b\u5904\u6709\u6700\u5c0f\u503cf(b)\uff1b
\u7b2c\u4e8c\u7ae0 \u57fa\u672c\u521d\u7b49\u51fd\u6570
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1\uff0e\u6839\u5f0f\u7684\u6982\u5ff5\uff1a\u4e00\u822c\u5730\uff0c\u5982\u679c \uff0c\u90a3\u4e48 \u53eb\u505a \u7684 \u6b21\u65b9\u6839\uff08n th root\uff09\uff0c\u5176\u4e2d >1\uff0c\u4e14 \u2208 *\uff0e
\u5f53 \u662f\u5947\u6570\u65f6\uff0c\u6b63\u6570\u7684 \u6b21\u65b9\u6839\u662f\u4e00\u4e2a\u6b63\u6570\uff0c\u8d1f\u6570\u7684 \u6b21\u65b9\u6839\u662f\u4e00\u4e2a\u8d1f\u6570\uff0e\u6b64\u65f6\uff0c \u7684 \u6b21\u65b9\u6839\u7528\u7b26\u53f7 \u8868\u793a\uff0e\u5f0f\u5b50 \u53eb\u505a\u6839\u5f0f\uff08radical\uff09\uff0c\u8fd9\u91cc \u53eb\u505a\u6839\u6307\u6570\uff08radical exponent\uff09\uff0c \u53eb\u505a\u88ab\u5f00\u65b9\u6570\uff08radicand\uff09\uff0e
\u5f53 \u662f\u5076\u6570\u65f6\uff0c\u6b63\u6570\u7684 \u6b21\u65b9\u6839\u6709\u4e24\u4e2a\uff0c\u8fd9\u4e24\u4e2a\u6570\u4e92\u4e3a\u76f8\u53cd\u6570\uff0e\u6b64\u65f6\uff0c\u6b63\u6570 \u7684\u6b63\u7684 \u6b21\u65b9\u6839\u7528\u7b26\u53f7 \u8868\u793a\uff0c\u8d1f\u7684 \u6b21\u65b9\u6839\u7528\u7b26\u53f7\uff0d \u8868\u793a\uff0e\u6b63\u7684 \u6b21\u65b9\u6839\u4e0e\u8d1f\u7684 \u6b21\u65b9\u6839\u53ef\u4ee5\u5408\u5e76\u6210\u00b1 \uff08 >0\uff09\uff0e\u7531\u6b64\u53ef\u5f97\uff1a\u8d1f\u6570\u6ca1\u6709\u5076\u6b21\u65b9\u6839\uff1b0\u7684\u4efb\u4f55\u6b21\u65b9\u6839\u90fd\u662f0\uff0c\u8bb0\u4f5c \u3002
\u6ce8\u610f\uff1a\u5f53 \u662f\u5947\u6570\u65f6\uff0c \uff0c\u5f53 \u662f\u5076\u6570\u65f6\uff0c
2\uff0e\u5206\u6570\u6307\u6570\u5e42
\u6b63\u6570\u7684\u5206\u6570\u6307\u6570\u5e42\u7684\u610f\u4e49\uff0c\u89c4\u5b9a\uff1a
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0\u7684\u6b63\u5206\u6570\u6307\u6570\u5e42\u7b49\u4e8e0\uff0c0\u7684\u8d1f\u5206\u6570\u6307\u6570\u5e42\u6ca1\u6709\u610f\u4e49
\u6307\u51fa\uff1a\u89c4\u5b9a\u4e86\u5206\u6570\u6307\u6570\u5e42\u7684\u610f\u4e49\u540e\uff0c\u6307\u6570\u7684\u6982\u5ff5\u5c31\u4ece\u6574\u6570\u6307\u6570\u63a8\u5e7f\u5230\u4e86\u6709\u7406\u6570\u6307\u6570\uff0c\u90a3\u4e48\u6574\u6570\u6307\u6570\u5e42\u7684\u8fd0\u7b97\u6027\u8d28\u4e5f\u540c\u6837\u53ef\u4ee5\u63a8\u5e7f\u5230\u6709\u7406\u6570\u6307\u6570\u5e42\uff0e
3\uff0e\u5b9e\u6570\u6307\u6570\u5e42\u7684\u8fd0\u7b97\u6027\u8d28
\uff081\uff09 �6�1 \uff1b
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1\u3001\u6307\u6570\u51fd\u6570\u7684\u6982\u5ff5\uff1a\u4e00\u822c\u5730\uff0c\u51fd\u6570 \u53eb\u505a\u6307\u6570\u51fd\u6570\uff08exponential function\uff09\uff0c\u5176\u4e2dx\u662f\u81ea\u53d8\u91cf\uff0c\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u4e3aR\uff0e
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2\u3001\u6307\u6570\u51fd\u6570\u7684\u56fe\u8c61\u548c\u6027\u8d28
a>1 0<a<1
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2\u3001\u5bf9\u6570\u51fd\u6570\u7684\u6027\u8d28\uff1a
a>1 0<a<1
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不过多抄抄公式也好，有利于今后学习的帮助
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