{"id":587,"date":"2022-08-27T22:19:37","date_gmt":"2022-08-27T14:19:37","guid":{"rendered":"https:\/\/damakey.com\/?p=587"},"modified":"2023-05-24T16:04:14","modified_gmt":"2023-05-24T08:04:14","slug":"%e7%a5%9e%e5%a5%87%e7%9a%84%e8%b6%85%e8%b6%8a%e6%95%b8e","status":"publish","type":"post","link":"https:\/\/damakey.com\/?p=587","title":{"rendered":"\u795e\u5947\u7684\u8d85\u8d8a\u6578e"},"content":{"rendered":"

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e<\/span>\u9019\u500b\u5e38\u6578\uff0c\u5728\u6578\u5b78\u88cf\uff0c\u53eb\u505a\u81ea\u7136\u5c0d\u6578\u7684\u5e95\uff0c\u70ba\u4e86\u7d00\u5ff5\u6578\u5b78\u5bb6\u5c24\u62c9\uff0c\u4e5f\u53eb\u5c24\u62c9\u6578\u3002<\/span><\/p>\n

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e<\/span>\u7684\u5b9a\u7fa9\u662f\uff1a\u7576<\/span>n—><\/span>\u7121\u9650\u5927\u6642\uff0c<\/span>(1+1\/n)^n=e=2.71828182846….<\/span><\/p>\n

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e<\/span>\u53ef\u4ee5\u900f\u904e\u628a<\/span>(1+1\/n)^n <\/span>\u505a\u4e8c\u9805\u5f0f\u5c55\u958b\u800c\u8a08\u7b97\u51fa\u4f86\uff0c<\/span>n<\/span>\u6108\u5927<\/span>(1+1\/n)^n<\/span>\u5c31\u6108\u903c\u8fd1<\/span>e<\/span>\u3002<\/span><\/p>\n

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(1+1\/n)^n <\/span>\u505a\u4e8c\u9805\u5f0f\u5c55\u958b<\/span>(<\/span>\u5176\u4e2d<\/span>C(nm)<\/span>\u4ee3\u8868<\/span>n!\/((n-m)!*m!))<\/span>\uff1a<\/span><\/p>\n

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=C(n0)*1^n*(1\/n)^0+C(n1)*1^(n-1)*(1\/n)^1+C(n2)*1^(n-2)*(1\/n)^2+C(n3)*1^(n-3)*(1\/n)^3+…+C(nn)*1^0*(1\/n)^n<\/span><\/p>\n

=1*1+n*(1\/n)+n!\/((n-2)!*2!))*(1\/n)^2+ n!\/((n-3)!*3!))*(1\/n)^3+…+1*(1\/n)^n<\/span><\/p>\n

=1+1+(n*(n-1))\/(2!n^2)+(n*(n-1)*(n-2))\/(3!*n^3)+…+(1\/n)^n<\/span><\/p>\n

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(<\/span>\u9019\u500b\u4e8c\u9805\u5f0f\u5c55\u958b\uff0c\u7dad\u57fa\u767e\u79d1\u6709\u6bd4\u8f03\u5bb9\u6613\u95b1\u8b80\u7684\u7684\u8868\u9054\u65b9\u5f0f<\/span>)<\/span><\/p>\n

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\u7576<\/span>n—><\/span>\u7121\u9650\u5927\u6642\uff0c\u524d\u5f0f\u8b8a\u6210\uff1a<\/span><\/p>\n

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e=1+1+1\/2+1\/6+…= 2.71828182846…<\/span><\/p>\n

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\u4ee5<\/span>e<\/span>\u70ba\u5e95\u7684\u5c0d\u6578\u5beb\u6210<\/span>Ln, <\/span>\u4ee5\u6709\u5225\u65bc\u4ee5<\/span>10<\/span>\u70ba\u5e95\u7684<\/span>Log<\/span><\/p>\n

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\u5728\u96d9\u66f2\u7dda\u4e0b\uff0c\u4ecb\u65bc<\/span>1<\/span>\u548c<\/span>e<\/span>\u4e4b\u9593\u7684\u9762\u7a4d\u525b\u597d\u70ba<\/span>1<\/span>\u3002\u628a\u96d9\u66f2\u7dda<\/span>1\/x<\/span>\u5f9e<\/span>1<\/span>\u5230<\/span>e<\/span>\u505a\u7a4d\u5206\uff1a<\/span>∫1\/x=ln|x| <\/span>\uff1b<\/span>ln(e)-ln(1)=1<\/span><\/p>\n

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e<\/span>\u4e5f\u53ef\u4ee5\u5b9a\u7fa9\u70ba\u968e\u5c64\u5012\u6578<\/span>1\/n!<\/span>\u7121\u7aae\u7d1a\u6578\u7684\u548c\uff1a<\/span><\/p>\n

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e=1\/0!+1\/1!+1\/2!+1\/3!+…+1\/n!<\/span><\/p>\n

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\u800c\u5176\u5be6\uff0c\u9019\u5c31\u662f<\/span>(1+1\/n)^n <\/span>\u4e8c\u9805\u5f0f\u5c55\u958b\u7576<\/span>n<\/span>\u8da8\u9032\u7121\u9650\u5927\u6642\u7684\u5f0f\u5b50\u5462\uff01<\/span><\/p>\n

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e<\/span>\u6709\u4e00\u500b\u7279\u9ede\uff0c\u662f\u4e00\u500b\u8d85\u8d8a\u6578\uff0c\u8d85\u8d8a\u4ee3\u6578\u6578\u7684\u610f\u601d\u3002<\/span><\/p>\n

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\u6574\u4fc2\u6578\u7684\u4ee3\u6578\u5f0f<\/span>a0X^n+a1X^n-1+…an-1X+anX(<\/span>\u5176\u4e2d<\/span>a0, a1,…,an<\/span>\u662f\u6574\u6578\uff0c<\/span>n<\/span>\u70ba\u81ea\u7136\u6578\uff0c\u4e14<\/span>a≠0)<\/span>\u7684\u6839\uff0c\u7a31\u70ba\u4ee3\u6578\u6578\u3002<\/span>e<\/span>\u4e0d\u662f\u4efb\u4f55\u4ee3\u6578\u5f0f\u7684\u6839\uff0c\u6240\u7a31\u4e4b\u70ba\u8d85\u8d8a\u4ee3\u6578\u6578\u7684\u8d85\u8d8a\u6578\u3002<\/span><\/p>\n

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\u5c24\u62c9\u9996\u5148\u63d0\u51fa\u300c\u8d85\u8d8a\u6578\u300d\u7684\u6982\u5ff5\uff0c\u4f46\u4e00\u76f4\u5230<\/span>100<\/span>\u5e74\u5f8c\u7684<\/span>1844<\/span>\u5e74\uff0c\u624d\u7531\u6cd5\u570b\u6578\u5b78\u5bb6\u8b49\u660e\u4e86\u8d85\u8d8a\u6578\u7684\u5b58\u5728\u3002<\/span><\/p>\n

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\u5c24\u62c9\u6700\u6709\u540d\u662f\u7d50\u5408\u4e86\u8907\u6578\u7684\u6982\u5ff5<\/span>(i=(-1)^1\/2; -1<\/span>\u958b\u6839\u865f<\/span>)<\/span>\u63d0\u51fa\u4e86\u5c24\u62c9\u516c\u5f0f<\/span> e^i<\/span>\ud835\udf45<\/span>+1=0<\/span>\u3002<\/span>1873<\/span>\u5e74\u6cd5\u570b\u6578\u5b78\u5bb6\u5384\u723e\u7c73\u7279\u501f\u52a9\u5c24\u62c9\u516c\u5f0f\uff0c\u8b49\u660e\u4e86<\/span>\ud835\udf45<\/span>\u4e5f\u662f\u8d85\u8d8a\u6578\uff0c\u4e0d\u662f\u4efb\u4f55\u6574\u4fc2\u6578\u4ee3\u6578\u65b9\u7a0b\u5f0f\u7684\u6839\u3002<\/span><\/p>\n

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\u5728<\/span>e<\/span>\u7684\u61c9\u7528\u4e0a\uff0c\u79d1\u5b78\u5bb6\u7528\u65bc\u8a08\u7b97\u706b\u7bad\u63a8\u529b\u3002<\/span><\/p>\n

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v=w*ln(z)<\/span>\uff0c\u5176\u4e2d<\/span> v<\/span>\u662f\u901f\u5ea6\uff1b<\/span>w<\/span>\u662f\u706b\u7bad\u767c\u52d5\u6a5f\u6392\u6c23\u901f\u5ea6\uff1b<\/span>z<\/span>\u662f\u706b\u7bad\u8d77\u521d\u8cea\u91cf\u548c\u767c\u52d5\u6a5f\u7684\u8cea\u91cf\u6bd4\u3002<\/span><\/p>\n

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\u53ea\u8981\u4e09\u7d1a\u706b\u7bad\u5373\u53ef\u7522\u751f\u8db3\u5920\u7684\u901f\u5ea6\uff1a<\/span>3wLn(z)=3*3Ln3~10<\/span>\u5343\u7c73<\/span>\/<\/span>\u79d2<\/span>>8 <\/span>\u5343\u7c73<\/span>\/<\/span>\u79d2\u7684\u7b2c\u4e00\u5b87\u5b99\u901f\u5ea6\u800c\u5230\u9054\u904b\u884c\u8ecc\u9053\u3002<\/span><\/p>\n

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\u5728\u9280\u884c\u696d\u88cf\uff0c\u8a08\u7b97\u5229\u606f\u7684\u516c\u5f0f\u662f\uff1a<\/span><\/p>\n

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A=p(1+r\/n)^nt<\/span><\/p>\n

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A:<\/span>\u672c\u5229\u548c\uff1b<\/span>p:<\/span>\u672c\u91d1\uff1b<\/span>r:<\/span>\u5e74\u5229\u7387\uff1b<\/span>n:<\/span>\u4e00\u5e74\u5167\u8a08\u7b97\u5229\u606f\u7684\u6b21\u6578\uff1b<\/span>t=<\/span>\u5b58\u9322\u5e74\u6578<\/span><\/p>\n

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\u5047\u8a2d\u7576\u671f\u521d\u5b58<\/span>1<\/span>\u5143<\/span>(p)<\/span>\uff0c\u5e74\u5229\u7387<\/span>100%(r)<\/span>\uff0c\u90a3\u9ebc\u5982\u679c\u5b58<\/span>1<\/span>\u5e74<\/span>(t)<\/span>\uff0c\u5957\u7528<\/span>e=(1+1\/n)^n  <\/span><\/span>\u9019\u500b\u516c\u5f0f\uff0c\u90a3\u9ebc\u4e00\u5e74\u7684\u672c\u5229\u548c<\/span>(A)<\/span>\u5c31\u662f<\/span>e<\/span>\u5143\u4e86\u3002<\/span>(e=2.7182818284590452353602)<\/span><\/p>\n

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\u7576\u7136\uff0c\u9019\u500b\u5047\u8a2d<\/span>100%<\/span>\u5229\u606f\u662f\u70ba\u4e86\u7522\u751f<\/span>e<\/span>\u9019\u500b\u672c\u5229\u548c\u7684\uff0c\u7528\u4f86\u8a8d\u8b58<\/span>e<\/span>\u9019\u500b\u8d85\u8d8a\u6578\u3002\u5982\u679c\u5229\u7387\u4e0d\u7b49\u65bc<\/span>100%<\/span>\uff0c\u5c31\u5f97\u56de\u5230<\/span>p(1+r\/n)^nt<\/span>\u9019\u500b\u8907\u5229\u516c\u5f0f\u53bb\u8a08\u7b97\u4e86\u3002<\/span><\/p>\n

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e<\/span>\u5728\u904b\u7528\u4e0a\u6700\u5ee3\u4eba\u77e5\u7684\u662f\u6307\u6578\u51fd\u6578<\/span> f(x)=e^x<\/span><\/p>\n

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\u7531\u65bc<\/span>f(x)<\/span>\u7684\u5fae\u5206<\/span>f’(x)<\/span>\u548c\u81ea\u8eab\u662f\u76f8\u7b49\u7684\uff0c\u53ef\u4ee5\u5beb\u6210<\/span>f(x)=f’(x)<\/span>\uff0c\u7e31\u4f7f\u628a\u6307\u6578\u51fd\u6578\u653e\u5927<\/span>k<\/span>\u500d\uff0c\u6210\u70ba<\/span>ke^x<\/span>\uff0c\u5b83\u5404\u5225\u7684\u5fae\u5206\u5c0e\u6578\u4e5f\u662f\u76f8\u540c\u7684\u3002<\/span>f(x)<\/span>\u4ee3\u8868\u51fd\u6578\u5728<\/span>x<\/span>\u9019\u500b\u9ede\u4e0a\u7684\u9ad8\u5ea6\uff0c\u800c<\/span>f’(x)<\/span>\u662f<\/span>x<\/span>\u9019\u500b\u9ede\u4e0a\u7684\u659c\u7387\uff0c\u5169\u8005\u76f8\u540c\u5c31\u662f\u6307\u6578\u51fd\u6578\u6700\u5927\u7684\u7279\u9ede\u4e86\u3002<\/span><\/p>\n

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*<\/span>\uff1a\u300a\u6578\u5b78\u516c\u5f0f\u7684\u7531\u4f86\u300b\uff0c\u7d00\u7d20\u96f2<\/span> <\/span>\u7b49<\/span><\/p>\n

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2022\/8\/26 <\/span>\u795e\u5947\u7684\u8d85\u8d8a\u6578<\/span>e Damakey<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

e\u9019\u500b\u5e38\u6578\uff0c\u5728\u6578\u5b78\u88cf\uff0c\u53eb\u505a\u81ea\u7136\u5c0d\u6578\u7684\u5e95\uff0c\u70ba\u4e86\u7d00\u5ff5\u6578\u5b78\u5bb6\u5c24\u62c9\uff0c…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"content-type":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-587","post","type-post","status-publish","format-standard","hentry","category-3"],"_links":{"self":[{"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/posts\/587","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/damakey.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=587"}],"version-history":[{"count":1,"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/posts\/587\/revisions"}],"predecessor-version":[{"id":19602,"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/posts\/587\/revisions\/19602"}],"wp:attachment":[{"href":"https:\/\/damakey.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/damakey.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/damakey.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}