{"id":2286,"date":"2024-09-04T20:55:39","date_gmt":"2024-09-04T12:55:39","guid":{"rendered":"http:\/\/www.jiaohuweike.online\/?p=2286"},"modified":"2024-09-04T20:55:39","modified_gmt":"2024-09-04T12:55:39","slug":"hsyldwt-5-4-2-3-2","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=2286","title":{"rendered":"\u5e42\u51fd\u6570\u3001\u6307\u6570\u51fd\u6570\u3001\u5bf9\u6570\u51fd\u6570"},"content":{"rendered":"\n

\u5e42\u51fd\u6570\u3001\u5206\u5f0f\u51fd\u6570\u7b49<\/h4>\n\n\n\n
1.\u89c2\u5bdf\u56fe\u8c61\uff0c\u8bf4\u8bf4m,n\u7684\u6b63\u8d1f\u3001\u5947\u5076\u5bf9\u5e42\u51fd\u6570y=x^{\\frac{n}{m}}\u56fe\u8c61\u7684\u5f71\u54cd\u3002~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
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\u7b54\u6848<\/summary>\n
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1.\\frac{n}{m}>0,\u51fd\u6570\u5728\u7b2c\u4e00\u8c61\u9650\u5355\u589e,\\frac{n}{m}<0,\u51fd\u6570\u5728\u7b2c\u4e00\u8c61\u9650\u5355\u51cf\u3002~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\2.n\u4e3a\u5947\u6570,m\u4e3a\u5076\u6570\u65f6\u4e3a\u975e\u5947\u975e\u5076\u51fd\u6570\uff1bm\u4e3a\u5947\u6570,n\u4e3a\u5076\u6570\u65f6\u4e3a\u5076\u51fd\u6570\uff1bn\u4e3a\u5947\u6570,~~~~~~\\\\m\u4e3a\u5947\u6570\u65f6\u4e3a\u5947\u51fd\u6570\u3002~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\n<\/details>\n\n\n\n
2.\u5e42\u51fd\u6570f(x)=(m^2+m-5)x^{m^2+2m-5}\u5728\u533a\u95f4(0,+\\infty)\u4e0a\u5355\u589e\uff0c\u6c42f(3)\u7684\u503c.~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1a27\uff1b\u63d0\u793a\uff1a\u5e42\u51fd\u6570y=x^a\u7684\u7cfb\u6570\u4e3a1\uff0c\u5728\u533a\u95f4(0,+\\infty)\u4e0a\u5355\u589e\uff0c\u5219a>0.~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
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3.\u8bbe\u51fd\u6570  f(x)=\\frac{a x+1}{x+2 a}  \u5728\u533a\u95f4  (-2,+\\infty)  \u4e0a\u662f\u589e\u51fd\u6570\uff0c\u6c42  a  \u7684\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1aa\\ge 1;\u63d0\u793a\uff1af(x)=a+\\frac{-2a^2+1}{x+2a},\\therefore \\left\\{\\begin{matrix}\n -2a\\le -2 & \\\\\n  -2a^2+1< 0&\n\\end{matrix}\\right.,\\therefore a\\ge 1.~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
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\u5bf9\u6570\u4e0d\u7b49\u5f0f<\/h4>\n\n\n\n
1.\u82e5\u65b9\u7a0b  4^{x}=\\log _{\\alpha} x  \u5728  \\left[0, \\frac{1}{2}\\right]  \u4e0a\u6709\u89e3,\u6c42\u5b9e\u6570  a  \u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1a(0,\\frac{\\sqrt{2}}{2}];\u6839\u636e\u56fe\u8c61\u53ef\u5f97\\log_a\\frac{1}{2}\\le2,\u89e3\u5bf9\u6570\u4e0d\u7b49\u5f0f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
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2.\u5df2\u77e5\u51fd\u6570  f(x)=\\left\\{\\begin{array}{l}2 x^{2}, x \\geqslant 0, \\\\ -2 x^{2}, x<0,\\end{array}\\right.  \u6c42\u4e0d\u7b49\u5f0f  f\\left(\\left(\\log _{2} x\\right)^{2}-3\\right)<4 f\\left(\\log _{2} x\\right)  \u7684\u89e3\u96c6.~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1a\\left(\\frac{1}{2}, 8\\right) \uff1b\u63d0\u793a\uff1a\u6b64\u51fd\u6570\u6ee1\u8db34f(t)=f(2t)\uff0c\u539f\u5f0f\\Rightarrow  f\\left(\\left(\\log _{2} x\\right)^{2}-3\\right)<~~~~~~~~~~~~ \\\\f\\left(2\\log _{2} x\\right) ,\u7531 f(x)\u56fe\u8c61\u53ef\u77e5f(x)\u5355\u589e,\\therefore \\left(\\log _{2} x\\right)^{2}-3<2\\log _{2} x,\\Rightarrow-1<\\log_2x<3.~~~<\/pre><\/div>\n\n\n\n
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3.\u6c42\u51fd\u6570  f(x)=\\sqrt{\\log _{0.5}(2 x-1)}  \u7684\u5b9a\u4e49\u57df.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1a[\\frac{1}{2},1];\u63d0\u793a\uff1a\\log _{0.5}(2 x-1)\\ge0,\u4e142x-1>0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
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4.\u5df2\u77e5\u51fd\u6570  f(x)  \u662f\u5b9a\u4e49\u5728  \\mathbf{R}  \u4e0a\u7684\u5076\u51fd\u6570, \u5f53  x \\leqslant 0  \u65f6,  f(x)  \u5355\u8c03\u9012\u51cf, \u6c42\u4e0d\u7b49\u5f0f~~~~~~~~~~~~~~~~~~~\\\\  f\\left(\\log _{\\frac{1}{3}}(2 x-5)\\right)>f\\left(\\log _{3} 8\\right)  \u7684\u89e3\u96c6.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1a\\left\\{x \\left\\lvert\\, \\frac{5}{2}< x< \\frac{41}{16}\\right.\\right.  \u6216  \\left.x >\\frac{13}{2}\\right\\} ;\u63d0\u793a\uff1a|f\\left(\\log _{\\frac{1}{3}}(2 x-5)\\right)|>|\\log _{3} 8 |.~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
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\u6bd4\u8f83\u5927\u5c0f<\/h4>\n\n\n\n
1.\u82e5  a=1.01^{0.5}, b=1.01^{0.6}, c=0.6^{0.5} , \u5219a, b, c \u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1ab>a>c;\u63d0\u793a\uff1a\u7531\u51fd\u6570f(x)=1.01^x,\\Rightarrow a< b;\u7531\u51fd\u6570f(x)=x^{0.5},\\Rightarrow a>c.~~~~~<\/pre><\/div>\n\n\n\n
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2.\u6bd4\u8f83\\left(\\frac{2}{3}\\right)^{\\frac{3}{4}}\u4e0e\\left(\\frac{3}{4}\\right)^{\\frac{2}{3}} \u7684\u5927\u5c0f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1a\\left(\\frac{2}{3}\\right)^{\\frac{3}{4}}<\\left(\\frac{3}{4}\\right)^{\\frac{2}{3}} ;\u63d0\u793a\uff1a\u6cd5\u4e00\u3001\u63d2\u5165\u4e2d\u95f4\u6570\\left(\\frac{2}{3}\\right)^{\\frac{2}{3}}\u6216\\left(\\frac{3}{4}\\right)^{\\frac{3}{4}};\u6cd5\u4e8c\u3001\u4e24\u8fb9\u53d6~~~~~~~\\\\\u5bf9\u6570\uff0c\u53ea\u9700\u8bc1\\ln\\left(\\frac{2}{3}\\right)^{\\frac{3}{4}}<\\ln\\left(\\frac{3}{4}\\right)^{\\frac{2}{3}},\u5229\u7528\u51fd\u6570f(x)=\\frac{\\ln x}{x}\u7684\u5355\u8c03\u6027.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
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3.\u6bd4\u8f83\\pi^3\u4e0e3^\\pi\u7684\u5927\u5c0f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1a\\pi^3<3^\\pi;\u63d0\u793a\uff1a\u4eff\u7167\u4e0a\u9898\u53d6\u4e2d\u95f4\u91cf3^3\u6216\\pi^{\\pi}\u90fd\u884c\u4e0d\u901a\uff01\u53ef\u4ee5\u4e24\u8fb9\u53d6\u5bf9\u6570\u3002\u8981\u8bc1~~~~~\\\\\\pi^3<3^\\pi\uff0c\u53ea\u9700\\ln \\pi^3<\\ln3^\\pi,\u53733\\ln \\pi<\\pi\\ln3,\u53ea\u9700\\frac{\\ln{\\pi}}{\\pi}<\\frac{\\ln{3}}{3}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n
4.\u6bd4\u8f83\\log_32\u4e0e\\log_43\u7684\u5927\u5c0f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
\u7b54\u6848<\/summary>\n
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\u7b54\u6848\uff1a\\log_32>\\log_43;\u63d0\u793a\uff1a\u6cd5\u4e00\u3001\u4e24\u6570\u4f5c\u6bd4\u5f97\\frac{\\ln2}{\\ln3}\\cdot\\frac{\\ln4}{\\ln3}\uff0c\u5206\u5b50\\ln2\\cdot\\ln4\\le~~~~~~~~~~~~~~~~~\\\\(\\frac{\\ln2+\\ln4}{2})^2=(\\frac{\\ln8}{2})^2=(\\ln \\sqrt8)^2<(\\ln3)^2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n
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\u5e42\u3001\u6307\u3001\u5bf9\u51fd\u6570\u7684\u57fa\u672c\u8fd0\u7b97\u53ca\u6027\u8d28<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-2286","post","type-post","status-publish","format-standard","hentry","category-hanshu"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/2286","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2286"}],"version-history":[{"count":0,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/2286\/revisions"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2286"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}