{"id":4146,"date":"2025-09-28T18:14:53","date_gmt":"2025-09-28T10:14:53","guid":{"rendered":"http:\/\/47.95.222.19\/?p=4146"},"modified":"2025-12-13T09:30:10","modified_gmt":"2025-12-13T01:30:10","slug":"hsds","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=4146","title":{"rendered":"\u51fd\u6570\u5bfc\u6570"},"content":{"rendered":"\n<div class=\"wp-block-stackable-call-to-action stk-block-call-to-action stk-block stk-3960b93 is-style-default\" data-v=\"2\" data-block-id=\"3960b93\"><style>.stk-3960b93 .stk-block-call-to-action__content{min-height:var(--stk--preset--block-height--none, 0px) !important;max-width:1500px !important;min-width:auto !important;}<\/style><div class=\"stk-block-call-to-action__content stk-content-align stk-3960b93-column stk-container stk-3960b93-container stk-hover-parent\"><div class=\"has-text-align-center stk-block-content stk-inner-blocks stk-3960b93-inner-blocks\">\n<div class=\"wp-block-stackable-heading stk-block-heading stk-block-heading--v2 stk-block stk-eeed53d\" id=\"\u558a\u4f60\u6765\u8bb2\u9898\uff01\" data-block-id=\"eeed53d\"><style>.stk-eeed53d .stk-block-heading__text{color:#0693e3 !important;}<\/style><h3 class=\"stk-block-heading__text has-text-color\">\u558a\u4f60\u6765\u8bb2\u9898\uff01<\/h3><\/div>\n\n\n\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-245933c\" data-block-id=\"245933c\"><style>.stk-245933c .stk-block-text__text{color:#0693e3 !important;}<\/style><p class=\"stk-block-text__text has-text-color\">\u628a\u77e5\u8bc6\u8bb2\u7ed9\u522b\u4eba\u662f\u6700\u9ad8\u6548\u7684\u5b66\u4e60\u65b9\u6cd5\uff01\u5b66\u4e60\u91d1\u5b57\u5854\u7406\u8bba\u548c\u8d39\u66fc\u5b66\u4e60\u6cd5\u5df2\u5370\u8bc1\u4e86\u8fd9\u4e00\u70b9\u3002\u5494\u5494\u6765\u8bb2\u4e3a\u4f60\u63d0\u4f9b\u4e00\u4e2a\u5e73\u53f0\uff0c\u8bf7\u4f60\u6765\u8bb2\u9898\uff0c\u5e76\u5c06\u89e3\u9898\u8fc7\u7a0b\u5f55\u5236\u51fa\u6765\uff0c\u8ba9\u4f60\u56e0\u2018\u5206\u4eab\u77e5\u8bc6\u2019\u800c\u8fdb\u6b65\uff0c\u8ba9\u77e5\u8bc6\u56e0\u2018\u88ab\u5206\u4eab\u2019\u800c\u66f4\u6709\u4ef7\u503c\u3002<\/p><\/div>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-56c6eb0\" data-block-id=\"56c6eb0\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-b01f8c8\" data-block-id=\"b01f8c8\"><style>.stk-b01f8c8 {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}.stk-b01f8c8 .stk-button{background:#0693e3 !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u67e5\u770b\u8981\u6c42<\/span><\/a><\/div>\n<\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-file alignright\"><a id=\"wp-block-file--media-b544b574-561f-4d95-b21a-5f9e61c7fba4\" href=\"http:\/\/jhwk.online\/wp-content\/uploads\/2025\/09\/\u4ea4\u4e92\u5fae\u8bfe\u5b66\u751f\u63a2\u7a76\u95ee\u9898\u2014\u2014\u51fd\u6570\u5bfc\u6570\u90e8\u5206-1.pdf\">\u9898\u76ee\u4e0b\u8f7d<\/a><\/div>\n\n\n\n<h5>\u9898\u76ee1<\/h5>\n<p>\u5df2\u77e5\u51fd\u6570\\( f(x) = x^2 &#8211; 2a\\ln x + 1 \\)\uff0c\\( a \\in R \\)\u3002<p>\n<p>\uff081\uff09\u5f53\\( a = -1 \\)\u65f6\uff0c\u8bbe\u66f2\u7ebf\\( y = f(x) \\)\u5728\\( x = 1 \\)\u5904\u7684\u5207\u7ebf\u4e3a\\( l \\)\uff0c\u6c42\\( l \\)\u4e0e\u66f2\u7ebf\\( y = f(x) \\)\u7684\u516c\u5171\u70b9\u4e2a\u6570\uff1b<\/p>\n<p>\uff082\uff09\u5f53\\( a > 0 \\)\u65f6\uff0c\u82e5\\( \\forall x_1, x_2 \\in [1, e] \\)\uff0c\\( |f(x_1) &#8211; f(x_2)| < e^2 + 1 \\)\u6052\u6210\u7acb\uff0c\u6c42\u5b9e\u6570\\( a \\)\u7684\u53d6\u503c\u8303\u56f4\u3002<\/p>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-903559f\" data-block-id=\"903559f\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-55da94f\" data-block-id=\"55da94f\"><style>.stk-55da94f {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4559\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u8bb2\u8bc4\u89c6\u9891<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-palette-color-2-color has-alpha-channel-opacity has-palette-color-2-background-color has-background is-style-wide\"\/>\n\n\n\n<h5>\u9898\u76ee2<\/h5>\n<p>\u5df2\u77e5\\( f(x) = x\\sin x + a\\cos x \\)\uff0c\\( x = \\pi \\)\u662f\u51fd\u6570\\( g(x) = f'(x) \\)\u7684\u6781\u5c0f\u503c\u70b9\u3002<\/p>\n<p>\uff081\uff09\u6c42\u5b9e\u6570\\( a \\)\u7684\u503c\uff1b<\/p>\n<p>\uff082\uff09\u8ba8\u8bba\u51fd\u6570\\( f(x) \\)\u5728\u533a\u95f4\\((-2\\pi, 2\\pi)\\)\u5185\u7684\u96f6\u70b9\u4e2a\u6570\u3002<\/p>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-99afb23\" data-block-id=\"99afb23\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-6353a5c\" data-block-id=\"6353a5c\"><style>.stk-6353a5c {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4187\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u6cd51\u3001\u8bb2\u8bc4\u89c6\u9891<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-6be9131\" data-block-id=\"6be9131\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-027c525\" data-block-id=\"027c525\"><style>.stk-027c525 {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4550\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u6cd52\u3001\u8bb2\u8bc4\u89c6\u9891<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-palette-color-2-color has-alpha-channel-opacity has-palette-color-2-background-color has-background is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-7748638\" data-block-id=\"7748638\"><p class=\"stk-block-text__text\"><\/p><\/div>\n\n\n\n<h5>\u9898\u76ee3<\/h5>\n<p>\u5df2\u77e5\u51fd\u6570\\( f(x)=x(1-\\ln x) \\)\u7684\u5355\u8c03\u6027\uff1b<\/p>\n<p>(1)\u8ba8\u8bba\\( f(x) \\)\u7684\u5355\u8c03\u6027\uff1b<\/p>\n<p>(2)\u8bbe\\( a, b \\)\u4e3a\u4e24\u4e2a\u4e0d\u76f8\u7b49\u7684\u6b63\u6570\uff0c\u4e14\\( b\\ln a &#8211; a\\ln b = a &#8211; b \\)\uff0c\u8bc1\u660e\uff1a\\( 2 <\\displaystyle \\frac{1}{a} + \\frac{1}{b} < e \\)\u3002<\/p>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-79f9c30\" data-block-id=\"79f9c30\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-135fd14\" data-block-id=\"135fd14\"><style>.stk-135fd14 {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4370\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u8bb2\u8bc4\u89c6\u9891<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-palette-color-2-color has-alpha-channel-opacity has-palette-color-2-background-color has-background is-style-wide\"\/>\n\n\n\n<h5>\u9898\u76ee4<\/h5>\n<p>\u5df2\u77e5\u51fd\u6570\\( f(x)= e^{x\\cos x} \\)\uff08\\( e \\)\u4e3a\u81ea\u7136\u5bf9\u6570\u7684\u5e95\u6570\uff09<\/p>\n\n<p>(1)\u6c42\u51fd\u6570\\( f(x) \\)\u5728\u70b9\\((0,f(0))\\)\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\uff1b<\/p>\n\n<p>(2)\u82e5\u8bb0\\( g(x)=-x^{3}-3x\\cdot \\cos x+(a+3)x \\)\uff0c\u82e5\\(\\forall x\\in [0,1] \\)\uff0c\u6709\\( f(x)\\leq e^{g(x)} \\)\uff0c\u6c42\\( a \\)\u7684\u53d6\u503c\u8303\u56f4\uff1b<\/p>\n\n<p>(3)\u8bbe\\( n\\in N^{*} \\)\uff0c\u4e14\\( n\\geq 2 \\)\uff0c\u8bc1\u660e\uff1a\\( \\cos1+\\cos\\displaystyle\\frac{2}{3}\\)+\\(\\cos\\displaystyle\\frac{1}{2}\\)+\\(\\cos\\displaystyle\\frac{2}{5}\\)+\\(\\dots+\\cos\\displaystyle\\frac{2}{n} < n-\\displaystyle\\frac{3}{2}\\)+\\(\\displaystyle\\frac{1}{n+1} \\)\uff0e<\/p>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-f4f76db\" data-block-id=\"f4f76db\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-ddccbbe\" data-block-id=\"ddccbbe\"><style>.stk-ddccbbe {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4448\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u8bb2\u8bc4\u89c6\u9891<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-palette-color-2-color has-alpha-channel-opacity has-palette-color-2-background-color has-background is-style-wide\"\/>\n\n\n\n<h5>\u9898\u76ee5<\/h5>\n\u8bbe\u51fd\u6570\\( f(x)=x^{2}(e^{x}-a) \\)<p>\n(1)\u5f53\\( a=0 \\)\u65f6,\u6c42\u66f2\u7ebf\\( y=f(x) \\)\u5728\\( (1,f(1)) \\)\u5904\u7684\u5207\u7ebf\u65b9\u7a0b.<p>\n(2)\u82e5\\( f(x) \\)\u662f\u589e\u51fd\u6570,\u6c42\\( a \\)\u7684\u503c.<p>\n(3)\u5f53\\( 0\\lt a\\lt 1 \\)\u65f6,\u8bbe\\( x_{0} \\)\u4e3a\\( f(x) \\)\u7684\u6781\u5927\u503c\u70b9,\u8bc1\u660e\\( 0\\lt f(x_{0})\\lt \\displaystyle\\frac{4}{e} \\).<p>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-3a8a2f6\" data-block-id=\"3a8a2f6\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-e86c6b3\" data-block-id=\"e86c6b3\"><style>.stk-e86c6b3 {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4667\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u8bb2\u8bc4\u89c6\u9891<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-palette-color-2-color has-alpha-channel-opacity has-palette-color-2-background-color has-background is-style-wide\"\/>\n\n\n\n<h5>\u9898\u76ee6<\/h5>\n\u5df2\u77e5\u51fd\u6570 \\(f(x) = a \\ln x &#8211; \\displaystyle \\frac{2}{x}\\)\uff0c\\(g(x) = \\displaystyle \\frac{e^x &#8211; 1}{x}\\)\uff0c\\(a \\in \\mathbb{R}\\)\u3002  \u5f53 \\(a = 1\\) \u65f6\uff0c\u6c42\u8bc1\uff1a\u5bf9\u4efb\u610f \\(x \\in (0, +\\infty)\\)\uff0c\u6052\u6709 \\(g(x) > f(x) + \\displaystyle \\frac{2 &#8211; \\cos x}{x}\\) \u6210\u7acb\u3002\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-4d71297\" data-block-id=\"4d71297\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-70c16ca\" data-block-id=\"70c16ca\"><style>.stk-70c16ca {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4851\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u8bb2\u8bc4\u89c6\u9891<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-palette-color-2-color has-alpha-channel-opacity has-palette-color-2-background-color has-background is-style-wide\"\/>\n\n\n\n<h5>\u9898\u76ee7<\/h5>\n<p>\u5df2\u77e5\u51fd\u6570$f(x)=xe^{x}-\\displaystyle \\frac {1}{2}ax^{2}-ax(a\u2208R).$\n<p>(1) \u8ba8\u8bba$f(x)$\u7684\u5355\u8c03\u6027\uff1b\n<p>(2) \u5f53$a>0$\u65f6\uff0c\u8bbe$f(x)$\u7684\u6781\u5927\u503c\u4e3a$g(a)$\uff0c\u6c42\u8bc1\uff1a$g(a)\u2265 -\\displaystyle \\frac {2}{e^{2}}.$\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-8587fea\" data-block-id=\"8587fea\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-65eefd9\" data-block-id=\"65eefd9\"><style>.stk-65eefd9 {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;border-style:solid !important;border-top-width:0px !important;border-right-width:0px !important;border-bottom-width:0px !important;border-left-width:0px !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4878\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u8bb2\u8bc4\u89c6\u9891<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-palette-color-2-color has-alpha-channel-opacity has-palette-color-2-background-color has-background is-style-wide\"\/>\n\n\n\n \n","protected":false},"excerpt":{"rendered":"<p>\u558a\u4f60\u6765\u8bb2\u9898\uff01 \u628a\u77e5\u8bc6\u8bb2\u7ed9\u522b\u4eba\u662f\u6700\u9ad8\u6548\u7684\u5b66\u4e60\u65b9\u6cd5\uff01\u5b66\u4e60\u91d1\u5b57\u5854\u7406\u8bba\u548c\u8d39\u66fc\u5b66\u4e60\u6cd5\u5df2\u5370\u8bc1\u4e86\u8fd9\u4e00\u70b9\u3002\u5494\u5494\u6765\u8bb2\u4e3a\u4f60\u63d0\u4f9b\u4e00\u4e2a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[71],"tags":[70],"class_list":["post-4146","post","type-post","status-publish","format-standard","hentry","category-tzzy","tag-70"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4146","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=4146"}],"version-history":[{"count":88,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4146\/revisions"}],"predecessor-version":[{"id":4889,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4146\/revisions\/4889"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4146"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}