{"id":4171,"date":"2015-01-03T20:56:52","date_gmt":"2015-01-03T20:56:52","guid":{"rendered":"http:\/\/eltawil.org\/sciencewonders\/?p=4171"},"modified":"2015-01-03T22:44:10","modified_gmt":"2015-01-03T22:44:10","slug":"%d9%82%d8%b5%d8%a9-%d8%b9%d8%af%d8%af-%d8%a3%d9%88%d9%8a%d9%84%d8%b1-e","status":"publish","type":"post","link":"https:\/\/eltawil.org\/sciencewonders\/?p=4171","title":{"rendered":"\u0642\u0635\u0629 \u0639\u062f\u062f \u0623\u0648\u064a\u0644\u0631 e"},"content":{"rendered":"

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\"\u0637\u0631\u064a\u0642\u0629<\/a>

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\u0648\u062d\u0635\u0644 \u0646\u0627\u0628\u064a\u064a\u0631 \u0639\u0644\u0649 \u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a\u0647 \u0628\u0637\u0631\u064a\u0642\u0629 \u0639\u062c\u064a\u0628\u0629 \u0648\u0635\u0641\u0647\u0627 \u0641\u0649 \u0643\u062a\u0627\u0628\u0647. \u0627\u0641\u062a\u0631\u0636 \u0646\u0627\u0628\u064a\u064a\u0631 \u0643\u0645\u0627 \u0628\u0627\u0644\u0631\u0633\u0645 \u062e\u0637 \u0645\u0633\u062a\u0642\u064a\u0645 \u0630\u0627 \u0637\u0648\u0644 \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u064a\u0648\u062c\u062f \u0627\u0633\u0641\u0644\u0647 \u0642\u0637\u0639\u0629 \u0645\u0633\u062a\u0642\u064a\u0645\u0629 \u0645\u062d\u062f\u0648\u062f\u0629 \u0627\u0644\u0637\u0648\u0644 \u0637\u0648\u0644\u0647\u0627 \u0645\u062b\u0644\u0627 \u0639\u0634\u0631\u0629 \u0645\u0644\u064a\u0648\u0646 \u0645\u062a\u0631 \u0645\u0648\u0627\u0632\u064a\u0629 \u0644\u0644\u062e\u0637 \u0627\u0644\u0639\u0644\u0648\u064a. \u0648\u0641\u0627\u0626\u062f\u0629 \u0627\u0644\u0631\u0642\u0645 \u0627\u0644\u0643\u0628\u064a\u0631 \u062c\u0639\u0644 \u0627\u0644\u0646\u0627\u062a\u062c \u0639\u0627\u0644\u0649 \u0627\u0644\u062f\u0642\u0629. \u0644\u0646\u0641\u0631\u0636 \u0627\u0646\u0647 \u064a\u0648\u062c\u062f \u0639\u0644\u0649 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 \u0648\u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u0629 \u062c\u0633\u0645\u0627\u0646 \u064a\u0646\u0632\u0644\u0642\u0627\u0646 \u0645\u0646 \u0627\u0644\u064a\u0633\u0627\u0631 \u0627\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646. \u0641\u0649 \u0628\u062f\u0627\u064a\u0629 \u0627\u0644\u062d\u0631\u0643\u0629 \u0643\u0627\u0646 \u0627\u0644\u062c\u0633\u0645\u0627\u0646 \u064a\u0648\u062c\u062f\u0627\u0646 \u0627\u0633\u0641\u0644 \u0628\u0639\u0636\u0647\u0645\u0627 \u062a\u0645\u0627\u0645\u0627. \u0644\u0646\u0641\u0631\u0636 \u0627\u0646 \u0627\u0644\u062c\u0633\u0645 \u0627\u0644\u0639\u0644\u0648\u064a \u064a\u062a\u062d\u0631\u0643 \u0628\u0633\u0631\u0639\u0629 \u062b\u0627\u0628\u062a\u0629 1 \u0645\u062a\u0631 \u0641\u0649 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0627\u0645\u0627 \u0627\u0644\u062c\u0633\u0645 \u0627\u0644\u0623\u062e\u0631 \u0641\u0627\u0646\u0647 \u064a\u0628\u062f\u0623 \u062d\u0631\u0643\u062a\u0647 \u0628\u0646\u0641\u0633 \u0627\u0644\u0633\u0631\u0639\u0629 \u062b\u0645 \u064a\u062a\u0628\u0627\u0637\u0623 \u062f\u0648\u0645\u0627 \u0628\u062d\u064a\u062b \u062a\u062a\u0646\u0627\u0633\u0628 \u0633\u0631\u0639\u062a\u0647 \u0645\u0639 \u0637\u0648\u0644 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0645\u062a\u0628\u0642\u064a\u0629 \u062d\u062a\u0649 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u0629. \u0648\u0627\u0637\u0644\u0642 \u0646\u0627\u0628\u064a\u064a\u0631 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0645\u0642\u0637\u0648\u0639\u0629 \u0639\u0644\u0649 \u0627\u0644\u062e\u0637 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u0649 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645. \u0628\u064a\u0646\u0645\u0627 \u0627\u0637\u0644\u0642 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0645\u062a\u0628\u0642\u064a\u0629 -\u0644\u064a\u0633\u062a \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0645\u0642\u0637\u0648\u0639\u0629- \u0639\u0644\u0649 \u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u0629 \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629. \u062b\u0645 \u0642\u0627\u0645 \u0646\u0627\u0628\u064a\u064a\u0631 \u0628\u0648\u0636\u0639 \u0642\u064a\u0645\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0644\u062a\u0649 \u062a\u0646\u0627\u0633\u0628 \u0642\u064a\u0645\u0629 \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0641\u0649 \u0639\u0645\u0648\u062f\u0647 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0623\u062e\u064a\u0631.<\/p>\n

\u0648\u0642\u062f \u0642\u0627\u0645 \u0646\u0627\u0628\u064a\u064a\u0631 \u0628\u0645\u0644\u0627\u064a\u064a\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0648\u0627\u062d\u062a\u0627\u062c \u062c\u062f\u0648\u0644\u0647 \u0627\u0644\u0645\u0648\u062c\u0648\u062f \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0649 20 \u0639\u0627\u0645\u0627 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644 \u0627\u0644\u0645\u062a\u0648\u0627\u0635\u0644. \u0641\u0649 \u062d\u0642\u064a\u0642\u0629 \u0627\u0644\u0627\u0645\u0631 \u0643\u0646\u062a \u0645\u062a\u0631\u062f\u062f\u0627 \u0641\u0649 \u0627\u062e\u062a\u064a\u0627\u0631 \u0639\u0646\u0648\u0627\u0646\u0627 \u0644\u0646\u0627\u0628\u064a\u064a\u0631. \u0641\u0649 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0627\u062e\u062a\u0631\u062a \u0644\u0647 \u0639\u0646\u0648\u0627\u0646 \u0627\u0644\u062d\u0627\u0633\u0628 \u0644\u0643\u0646 \u0631\u0628\u0645\u0627 \u064a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0627\u0641\u0636\u0644 \u0627\u0646 \u0646\u0637\u0644\u0642 \u0639\u0644\u064a\u0647 \u0627\u0644\u0645\u062b\u0627\u0628\u0631!<\/p>\n

\"\u062c\u062f\u0648\u0644<\/a>

\u062c\u062f\u0648\u0644 \u0646\u0627\u0628\u064a\u064a\u0631<\/p><\/div>\n

\u0648\u0623\u0631\u0642\u0627\u0645 \u0646\u0627\u0628\u064a\u064a\u0631 \u062a\u0639\u0637\u0649 \u0646\u0641\u0633 \u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0623\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0628\u0639\u062f \u0627\u0646 \u0646\u0642\u0633\u0645 \u0627\u0631\u0642\u0627\u0645 \u0627\u0644\u0639\u0645\u0648\u062f\u064a\u0646 \u0627\u0644\u0627\u0648\u0644 \u0648 \u0627\u0644\u062b\u0627\u0646\u0649 \u0639\u0644\u0649 10 \u0645\u0644\u064a\u0648\u0646. \u0648\u0628\u0639\u062f \u0627\u0646 \u0646\u0639\u0637\u0649 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0627\u0634\u0627\u0631\u0629 \u0633\u0627\u0644\u0628\u0629. \u0648\u0646\u0644\u0627\u062d\u0638 \u0627\u0646 \u0646\u0627\u0628\u064a\u064a\u0631 \u062d\u0634\u0631 \u0645\u0635\u0637\u0644\u062d \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0641\u0649 \u062d\u062f\u064a\u062b\u0647 \u0644\u0627\u0646\u0647 \u0643\u0627\u0646 \u064a\u0631\u064a\u062f \u062a\u0633\u0644\u064a\u0637 \u0627\u0643\u0628\u0631 \u0642\u062f\u0631 \u0645\u0646 \u0627\u0644\u0627\u0647\u062a\u0645\u0627\u0645 \u0639\u0644\u0649 \u0637\u0631\u064a\u0642\u062a\u0647.\u0641\u0647\u0648 \u0623\u0631\u0627\u062f \u0627\u0646 \u064a\u0624\u0643\u062f \u0627\u0646 \u0644\u062a\u0642\u0646\u064a\u062a\u0647 \u0627\u0647\u0645\u064a\u0629 \u0639\u0645\u0644\u064a\u0629 \u0641\u0649 \u0623\u0647\u0645 \u0645\u0648\u0636\u0648\u0639 \u0641\u0649 \u0630\u0644\u0643 \u0627\u0644\u0648\u0642\u062a \u0623\u0644\u0627 \u0648\u0647\u0648 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a.<\/p>\n

\u0644\u0646\u0631\u0649 \u0645\u062b\u0627\u0644\u0627 \u0639\u0645\u0644\u064a\u0627 \u0644\u0644\u062d\u0633\u0627\u0628 \u0628\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0646\u0627\u0628\u064a\u064a\u0631: \u0645\u062b\u0644\u0627 \u0644\u0648 \u0623\u0631\u062f\u0646\u0627 \u062d\u0633\u0627\u0628 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u0649 \u0644\u0636\u0631\u0628 \u0639\u0634\u0631\u0629 \u0645\u0644\u0627\u064a\u064a\u0646 \u0641\u0649 \u062e\u0645\u0633\u0629 \u0645\u0644\u0627\u064a\u064a\u0646:
\nsqrt(10000000 * 5 000 000)= 7071067.8<\/p>\n

\u0639\u0644\u064a\u0646\u0627 \u0627\u0646 \u0646\u0628\u062d\u062b \u0639\u0646 \u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0639\u0634\u0631\u0629 \u0645\u0644\u0627\u064a\u064a\u0646 \u0641\u0649 \u062c\u062f\u0648\u0644 \u0646\u0627\u0628\u064a\u064a\u0631 \u0648\u0643\u0630\u0644\u0643 \u0646\u0628\u062d\u062b \u0639\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0644\u062a\u0649 \u062a\u0642\u0627\u0628\u0644 5 \u0645\u0644\u0627\u064a\u064a\u0646 \u062b\u0645 \u0646\u062c\u0645\u0639 \u0627\u0644\u0642\u064a\u0645\u062a\u064a\u0646 \u0648\u0646\u0642\u0633\u0645 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0639\u0644\u0649 2 . \u0627\u0644\u0627\u0646 \u0646\u0635\u0644 \u0627\u0644\u0649 \u0627\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u0627\u062e\u064a\u0631\u0629 \u062d\u064a\u062b \u0646\u0628\u062d\u062b \u0639\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0644\u062a\u0649 \u062d\u0635\u0644\u0646\u0627 \u0639\u0644\u064a\u0647\u0627 \u0641\u0649 \u062e\u0627\u0646\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0648\u0646\u0642\u0631\u0623 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629 \u0641\u0649 \u0627\u0644\u0639\u0645\u0648\u062f \u0627\u0644\u0623\u0648\u0644. \u0627\u0648<\/p>\n

log_nap(10000000)+log_nap(5000000)=0+693147=6931471
\n6931471\/2 = 3465735
\n\u0648\u0628\u0627\u0644\u0628\u062d\u062b \u0641\u0649 \u0627\u0644\u062c\u062f\u0648\u0644 \u0645\u0631\u0629 \u0627\u062e\u0631\u0649 \u0646\u062c\u062f \u0627\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 \u0647\u0649 7071068 \u0648\u0647\u0649 \u0646\u0641\u0633 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0644\u062a\u0649 \u0646\u062d\u0635\u0644 \u0639\u0644\u064a\u0647\u0627 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0644\u0623\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u062a\u0642\u0631\u064a\u0628\u0627. \u0648\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062c\u0645\u0639 \u0648 \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 2\u00a0 \u0647\u0649 \u0639\u0645\u0644\u064a\u0627\u062a \u0633\u0647\u0644\u0629 \u0628\u0627\u0644\u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u0627\u0644\u0636\u0631\u0628 \u062b\u0645 \u0627\u0644\u0628\u062d\u062b \u0639\u0646 \u062c\u0630\u0631.<\/p>\n

\u0644\u0643\u0646 \u0645\u0627 \u0627\u0644\u0633\u0631 \u0641\u0649 \u0623\u0646 \u0637\u0631\u064a\u0642\u0629 \u0646\u0627\u0628\u064a\u064a\u0631 \u062a\u0639\u0637\u064a \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0633\u0644\u064a\u0645\u0629\u061f \u0627\u0644\u0627\u062c\u0627\u0628\u0629 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u062e\u0648\u0627\u0635 \u062d\u0633\u0627\u0628 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0627\u0644\u0644\u062a\u0649 \u062a\u062d\u0648\u0644 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0649 \u062c\u0645\u0639 \u0648 \u0627\u0644\u0642\u0633\u0645\u0629 \u0627\u0644\u0649 \u0637\u0631\u062d \u0648\u0627\u0644\u0631\u0641\u0639 \u0627\u0644\u0649 \u0627\u0633 \u0627\u0644\u0649 \u0636\u0631\u0628. \u0628\u0645\u0639\u0646\u0649 \u0623\u0646
\nlog(a*b) = log(a) +log(b) 1
\nlog(a\/b) = lob(a) -log(b) 2
\nlog(a^b) = b*log(a) 3<\/p>\n

\u0644\u0643\u0646 \u0639\u0644\u064a\u0646\u0627 \u0623\u0646 \u0646\u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0639\u0646\u062f \u0646\u0627\u0628\u064a\u064a\u0631 \u0643\u0627\u0646\u062a \u0645\u062c\u0631\u062f \u0627\u0631\u0642\u0627\u0645 \u0645\u0633\u0627\u0639\u062f\u0629 \u0644\u062a\u0633\u0647\u064a\u0644 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628. \u0648\u0644\u0648 \u0627\u0633\u062a\u062e\u062f\u0645\u0646\u0627 \u0627\u0644\u0629 \u0632\u0645\u0646 \u0648\u0631\u062c\u0639\u0646\u0627 \u0627\u0644\u0649 \u0646\u0627\u0628\u064a\u064a\u0631 \u0648\u0642\u0644\u0646\u0627 \u0644\u0647 \u0645\u0627 \u0646\u0639\u0631\u0641\u0647 \u0639\u0646 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0627\u0644\u064a\u0648\u0645 \u0648\u0627\u0646\u0647\u0627 \u062f\u0627\u0644\u0629 \u0648\u062a\u062d\u062f\u064a\u062f\u0627 \u0627\u0646\u0647\u0627 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633 \u0644\u0644\u062b\u0627\u0628\u062a e \u0644\u0646\u0638\u0631 \u0627\u0644\u064a\u0646\u0627 \u0628\u0627\u0633\u062a\u063a\u0631\u0627\u0628 \u0648\u0631\u0628\u0645\u0627 \u0637\u0644\u0628 \u0644\u0646\u0627 \u0637\u0628\u064a\u0628. \u0641\u0649 \u0627\u062d\u0633\u0646 \u0627\u0644\u0627\u062d\u0648\u0627\u0644 \u0644\u0638\u0646 \u0623\u0646 \u062c\u0647\u0644\u0646\u0627 \u0645\u0646 \u0637\u0631\u0627\u0632 \u0641\u0631\u064a\u062f. \u0641\u0647\u0648 \u0635\u0627\u062d\u0628 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0648\u0645\u0639\u0637\u064a\u0647\u0627 \u0627\u0633\u0645\u0647\u0627 \u0648\u0644\u0643\u0646\u0647 \u0644\u0627 \u064a\u0639\u0631\u0641 \u0627\u0649 \u0634\u0626 \u0639\u0645\u0627 \u0646\u062a\u062d\u062f\u062b \u0639\u0646\u0647 \u0648\u0644\u0645 \u064a\u0643\u0646 \u0630\u0644\u0643 \u0647\u0648 \u0647\u062f\u0641\u0647.<\/p>\n

\u0648\u0643\u0627\u0646\u062a \u0644\u0637\u0631\u064a\u0642\u0629 \u0646\u0627\u0628\u064a\u064a\u0631 \u0627\u0647\u0645\u064a\u0629 \u0639\u0645\u0644\u064a\u0629 \u0643\u0628\u064a\u0631\u0629. \u0648\u0627\u0635\u0628\u062d\u062a \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0631\u0633\u0645\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0627\u0631\u0642\u0627\u0645 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0648\u0627\u0644\u0645\u0639\u0642\u062f\u0629. \u0648\u0628\u0646\u0627\u0621 \u0639\u0644\u064a\u0647\u0627 \u062a\u0645 \u0635\u0646\u0627\u0639\u0629 \u0627\u0644\u0645\u0633\u0637\u0631\u0629 \u0627\u0644\u0645\u062a\u062d\u0631\u0643\u0629 \u0630\u0627\u062a \u0627\u0644\u0642\u064a\u0627\u0633 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0649. \u0648\u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0637\u0631\u0629 \u0643\u0627\u0646\u062a \u0627\u0644\u0627\u062f\u0627\u0629 \u0627\u0644\u0645\u062d\u0628\u0628\u0629 \u0644\u062f\u0649 \u0627\u0644\u0645\u0647\u0646\u062f\u0633\u064a\u0646 \u062d\u062a\u0649 \u0633\u0628\u0639\u064a\u0646\u064a\u0627\u062a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u0645\u0627\u0636\u064a. \u0644\u0643\u0646 \u0637\u0628\u0639\u0627 \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0637\u0631\u0629 \u0644\u0627 \u062a\u0633\u062a\u062e\u062f\u0645 \u0641\u0649 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u064a\u0648\u0645 \u0648\u0631\u0628\u0645\u0627 \u064a\u0643\u0648\u0646 \u0645\u0643\u0627\u0646\u0647\u0627 \u0627\u0644\u064a\u0648\u0645 \u0647\u0648 \u0627\u0644\u0645\u062a\u062d\u0641!<\/p>\n

\u0627\u0630\u0646 \u0628\u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0646\u0627\u0628\u064a\u064a\u0631 \u0647\u0648 \u0627\u0648\u0644 \u0645\u0646 \u0648\u0636\u0639 \u0628\u0639\u0636 \u0642\u064a\u0645 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0637\u0628\u064a\u0639\u0649 \u0627\u0644\u0627 \u0627\u0646\u0647 \u0644\u0645 \u064a\u0639\u0631\u0641 \u0627\u0644\u062b\u0627\u0628\u062a e . \u0648\u0644\u0630\u0644\u0643 \u0627\u0639\u062a\u0642\u062f \u0627\u0646 \u062a\u0633\u0645\u064a\u0629 \u0630\u0644\u0643 \u0627\u0644\u0639\u062f\u062f \u0628\u0627\u0644\u062b\u0627\u0628\u062a \u0627\u0644\u0646\u064a\u0628\u064a\u0631\u064a -\u0643\u0645\u0627 \u064a\u062c\u062f \u0627\u0644\u0623\u0646\u0633\u0627\u0646 \u0627\u062d\u064a\u0627\u0646\u0627 \u0641\u0649 \u0628\u0639\u0636 \u0627\u0644\u0645\u0635\u0627\u062f\u0631- \u0647\u0649\u00a0 \u062a\u0633\u0645\u064a\u0629 \u0644\u064a\u0633\u062a \u0641\u0649 \u0645\u062d\u0644\u0647\u0627 \u0627\u0628\u062f\u0627.<\/p>\n

\u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a:<\/strong> \u0627\u0645\u0627 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u0649 \u0641\u0647\u0648 \u0627\u0644\u0647\u0648\u0644\u0646\u062f\u064a \u0643\u0631\u064a\u0633\u062a\u064a\u0627\u0646 \u0647\u064a\u062c\u064a\u0646\u0632<\/a> Christiaan Huygens \u0627\u0644\u0644\u0630\u064a \u0639\u0627\u0634 \u0641\u0649 \u0627\u0644\u0641\u062a\u0631\u0629 \u0628\u064a\u0646 1629 \u062d\u062a\u0649 1695 \u0645\u064a\u0644\u0627\u062f\u064a\u0627. \u0648\u0647\u0648 \u0631\u064a\u0627\u0636\u0649 \u0648\u0641\u064a\u0632\u064a\u0627\u0626\u0649 \u0647\u0627\u0645. \u0627\u0645\u0627 \u0639\u0646\u0647 \u0646\u0639\u062a\u0647 \u0628\u0627\u0644\u062a\u062d\u0644\u064a\u0644\u0649 \u0641\u0644\u0627\u0646\u0647 \u0642\u0645 \u0628\u0645\u0642\u0627\u0631\u0628\u0629 \u0644\u0644\u062b\u0627\u0628\u062a e \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u00a0 analysis\u00a0 \u0623\u0648 \u062d\u0633\u0627\u0628 \u0627\u0644\u062f\u0648\u0627\u0644. \u062d\u064a\u062b \u0642\u0645 \u0647\u064a\u062c\u0646\u0632 \u0628\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u062a\u062d\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0648\u0627\u0644\u0645\u0647\u0645\u0629:
\nf(x) = 1\/x \u00a0 \u00a0 4<\/p>\n

\"\u0627\u0644\u0645\u0633\u0627\u062d\u0629<\/a>

\u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u062a\u0633\u0627\u0648\u0649 \u0642\u064a\u0645\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0637\u0628\u064a\u0639\u064a<\/p><\/div>\n

\u0648\u0643\u0645\u0627 \u0646\u0639\u0644\u0645 \u0627\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u0627\u0644\u0645\u062d\u0635\u0648\u0631\u0629 \u0628\u064a\u0646 \u0645\u062d\u0648\u0631 x \u0648\u0645\u0646\u062d\u0646\u0649 \u0627\u0644\u062f\u0627\u0644\u0629 \u0648\u062d\u062f\u064a\u0646 \u0645\u0639\u064a\u0646\u064a\u0646 \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0627\u0644\u062a\u0639\u0648\u064a\u0636\u00a0 \u0641\u0649 \u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0647\u0630\u064a\u0646 \u0627\u0644\u062d\u062f\u064a\u0646 \u062b\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0641\u0627\u0631\u0642 . \u0648\u0643\u0645\u0627 \u0646\u0639\u0644\u0645 \u0627\u0646 \u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062f\u0627\u0644\u0629\u00a0 1\/x\u00a0 \u064a\u0633\u0627\u0648\u0649 lnx . \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u0649 \u0641\u0627\u0646 \u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u0627\u0644\u0645\u062d\u0635\u0648\u0631\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 1 \u0648 t\u00a0 \u0639\u0644\u0649 \u0645\u062d\u0648\u0631 x \u064a\u0633\u0627\u0648\u0649 \u062f\u0627\u0626\u0645\u0627 \u0644\u0648\u0639\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 t . \u0627\u0648 \u062a\u0641\u0635\u064a\u0644\u0627:<\/p>\n

Integral(1\/x) [1->t] =Ln(x) [1->t]\u00a0 = ln(t) -ln(1) = ln(t\/1) = ln(t) 5<\/p>\n

\u0648\u0647\u0630\u0627 \u0647\u0648 \u0645\u0627\u0648\u062c\u062f\u0647 \u0647\u064a\u062c\u0646\u0632. \u0641\u0642\u062f \u0648\u062c\u062f \u062f\u0627\u0626\u0645\u0627 \u0627\u0646 \u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u062a\u062d\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0628\u0646\u0642\u0637\u062a\u064a\u0646 \u0639\u0644\u0649 \u0645\u062d\u0648\u0631 x \u0648\u0627\u0644\u0646\u0642\u0637\u0629 1 \u0627\u062d\u062f\u0647\u0645\u0627 \u062a\u0633\u0627\u0648\u0649 \u062f\u0627\u0626\u0645\u0627 \u0642\u064a\u0645\u0629 \u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0646\u0627\u0628\u064a\u064a\u0631 \u0644\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0623\u062e\u0631\u0649. \u0628\u0644 \u0627\u0643\u062b\u0631 \u0645\u0646 \u0630\u0644\u0643 \u0643\u0627\u0646 \u0647\u064a\u062c\u0646\u0632 \u064a\u0628\u062d\u062b \u062a\u062d\u062f\u064a\u062f\u0627 \u0639\u0646 \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0644\u062a\u0649 \u062a\u062d\u0635\u0631 \u0628\u064a\u0646\u0647\u0627 \u0648\u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 1 \u0645\u0633\u0627\u062d\u0629 \u0642\u062f\u0631\u0647\u0627 \u0627\u0644\u0648\u062d\u062f\u0629. \u0648\u0643\u0645\u0627 \u0646\u0639\u0644\u0645\u00a0 \u0627\u0646 \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629 \u0644\u0627\u0628\u062f \u0627\u0646 \u064a\u0643\u0648\u0646 \u0627\u062d\u062f\u0627\u062b\u064a\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0645\u062d\u0648\u0631 x \u064a\u0633\u0627\u0648\u0649 e \u0644\u0623\u0646 ln(e) = 1
\n\u0627\u0630\u0646 \u0643\u0627\u0646 \u0647\u064a\u062c\u0646\u0632 \u064a\u062d\u0648\u0645 \u062d\u0648\u0644 e \u062d\u0648\u0645\u0627 \u0648\u0643\u0627\u062f \u0627\u0646 \u064a\u0635\u0644 \u0627\u0644\u064a\u0647 \u0648\u0644\u0643\u0646\u0647 \u0644\u064a\u0633 \u0647\u0648 \u0645\u0646 \u062d\u062f\u062f \u0642\u064a\u0645\u0629 \u0647\u0630\u0627 \u0627\u0644\u062b\u0627\u0628\u062a<\/p>\n

\u0627\u0644\u0628\u0646\u0643\u0649:<\/strong> \u0627\u0645\u0627 \u0627\u0644\u0628\u0646\u0643\u0649 \u0641\u0647\u0648 \u064a\u0623\u062a\u0649 \u0645\u0646 \u0633\u0648\u064a\u0633\u0631\u0627 \u0628\u0644\u062f \u0627\u0644\u0628\u0646\u0648\u0643 \u0648\u0647\u0648 \u064a\u0627\u0643\u0648\u0628 \u0628\u0631\u0646\u0648\u0644\u064a. Jakob Bernoulli . \u0648\u0647\u0648 \u064a\u0646\u062a\u0645\u0649 \u0627\u0644\u0649 \u0639\u0627\u0626\u0644\u0629 \u0628\u0631\u0646\u0648\u0644\u0649 \u0627\u0644\u0639\u0644\u0645\u064a\u0629 \u0627\u0644\u0634\u0647\u064a\u0631\u0629<\/a>. \u0648\u0639\u0627\u0634 \u0628\u0631\u0646\u0648\u0644\u0649 \u0641\u064a \u0627\u0644\u0641\u062a\u0631\u0629 \u0645\u0646 1654 \u062d\u062a\u0649 1705 \u0645\u064a\u0644\u0627\u062f\u064a\u0627. \u0648\u0643\u0627\u0646 \u0628\u0631\u0646\u0648\u0644\u064a \u0645\u0647\u062a\u0645\u0627 \u0628\u062d\u0633\u0627\u0628 \u0642\u064a\u0645\u0629 \u0627\u0644\u0641\u0627\u0626\u062f\u0629 \u0627\u0644\u0645\u0631\u0643\u0628\u0629. \u0648\u0643\u0627\u0646 \u064a\u0628\u062d\u062b \u0641\u0649 \u0627\u0644\u0642\u0636\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: \u0627\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0628\u0646\u0643 \u064a\u0639\u0637\u0649 \u0641\u0627\u0626\u062f\u0629 100% . \u062b\u0645 \u0627\u0648\u062f\u0639 \u0627\u0646\u0633\u0627\u0646 \u0641\u0631\u0646\u0643\u0627 \u0633\u0648\u064a\u0633\u0631\u064a\u0627 \u0641\u0649 \u0647\u0630\u0647 \u0627\u0644\u0628\u0646\u0643 \u0648\u062a\u0631\u0643\u0647 \u0644\u0645\u062f\u0629 \u0639\u0627\u0645 \u0641\u0643\u0645 \u0633\u0648\u0641 \u062a\u0635\u0628\u062d \u0642\u064a\u0645\u062a\u0647\u061f \u0637\u0628\u0639\u0627 \u062d\u0633\u0627\u0628 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645\u0629 \u0633\u0647\u0644 \u0648\u064a\u0633\u0627\u0648\u064a
\n1*(1+1) = 2
\n\u0623\u064a \u0641\u0631\u0646\u0643\u064a\u0646.\u0644\u0643\u0646 \u0645\u0627\u0630\u0627 \u0627\u0630\u0627 \u0643\u0627\u0646 \u0647\u0630\u0627 \u0627\u0644\u0628\u0646\u0643 \u0644\u0627\u064a\u0639\u0637\u064a \u0641\u0627\u0626\u062f\u0629 100% \u0641\u0649 \u0627\u0644\u0633\u0646\u0629 \u0648\u0644\u0643\u0646\u0647 \u064a\u0639\u0637\u0649 50% \u0645\u0631\u062a\u064a\u0646 \u0641\u0649 \u0627\u0644\u0633\u0646\u0629. \u0627\u064a\u0636\u0627 \u0627\u0644\u062d\u0633\u0627\u0628 \u0633\u0647\u0644 \u0648\u064a\u0633\u0627\u0648\u064a.
\n1*(1+0.5)*(1+0.5) = 1*1.5^2= 2.25
\n\u0648\u0645\u0627\u0630\u0627 \u0627\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0628\u0646\u0643 \u064a\u0648\u0632\u0639 \u0627\u0644\u0641\u0627\u0626\u062f\u0629 \u0628\u0634\u0643\u0644 \u0645\u062e\u062a\u0644\u0641 \u062a\u062d\u062f\u064a\u062f\u0627 8.33% \u0643\u0644 \u0634\u0647\u0631. \u0645\u0631\u0629 \u0627\u062e\u0631\u0649 \u062a\u0643\u0648\u0646 \u0627\u0644 100% \u0645\u0648\u0632\u0639\u0629\u00a0 \u0639\u0644\u0649 \u0627\u0644\u0627\u062b\u0646\u0649 \u0639\u0634\u0631 \u0634\u0647\u0631\u0627 \u0648\u0633\u062a\u0635\u0628\u062d \u0642\u064a\u0645\u0629 \u0627\u0644\u0641\u0631\u0646\u0643 \u0628\u0639\u062f \u0633\u0646\u0629 \u062a\u0633\u0627\u0648\u064a
\n1*(1+1\/12)^12 = 2.61 \u0641\u0631\u0646\u0643\u0627\u062a.
\n\u0648\u0645\u0627\u0630\u0627 \u0627\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0628\u0646\u0643 \u064a\u0648\u0632\u0639 \u0627\u0644\u0641\u0627\u0626\u062f\u0629 \u0641\u0649 \u0643\u0644 \u0627\u0644\u0623\u064a\u0627\u0645 \u0639\u0644\u0649 \u0645\u062f\u0627\u0631 \u0627\u0644\u0633\u0646\u0629. \u0627\u0630\u0646 \u0633\u0648\u0641 \u062a\u0643\u0648\u0646 \u0627\u0644\u0641\u0627\u0626\u062f\u0629
\n1*(1+1\/365)^365 = 2.71 . \u0648\u0645\u0627\u0630\u0627 \u0627\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0628\u0646\u0643 \u064a\u0648\u0632\u0639 \u0627\u0644\u0641\u0627\u0626\u062f\u0629 \u0643\u0644 \u0633\u0627\u0639\u0629 \u0628\u0644 \u0643\u0644 \u062b\u0627\u0646\u064a\u0629 \u0628\u0644 \u0643\u0644 \u0644\u062d\u0638\u0629 \u0627\u0630\u0646 \u0633\u062a\u0635\u0628\u062d \u0642\u064a\u0645\u0629 \u0627\u0644\u0641\u0631\u0646\u0643 \u062a\u0633\u0627\u0648\u0649 \u0642\u064a\u0645\u0629 \u0627\u0644\u062b\u0627\u0628\u062a e
\nlim(1+1\/n)^n[n->infinity]= e
\n\u0644\u0643\u0646 \u0628\u0631\u0646\u0648\u0644\u0649 \u0644\u0645 \u064a\u0633\u062a\u0637\u0639 \u0627\u0644\u062a\u0648\u0635\u0644 \u0628\u0646\u0641\u0633\u0647 \u0627\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645\u0629. \u0648\u0645\u0627\u062a\u0648\u0635\u0644 \u0627\u0644\u064a\u0647 \u0627\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 \u062a\u0646\u062d\u0635\u0631 \u0628\u064a\u0646 2 \u0648 3 .<\/p>\n

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\ne = 1 + 1\/1! + 1\/2! + 1\/3! + … 6<\/p>\n

\u0643\u0645\u0627 \u0627\u0643\u062a\u0634\u0641 \u0627\u0648\u064a\u0644\u0631 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062c\u0645\u064a\u0644\u0629 \u0641\u0649 \u0627\u0644\u0631\u0633\u0645 \u0639\u0644\u0649 \u0635\u0648\u0631\u0629 \u0643\u0633\u0631 \u0645\u0633\u062a\u0645\u0631 \u0648\u0627\u0644\u0644\u062a\u0649 \u0645\u0646\u0647\u0627 \u0646\u0633\u062a\u0637\u064a\u0639 \u0627\u0646 \u0646\u0631\u0649 \u0627\u0646 \u0647\u0630\u0627 \u0627\u0644\u062b\u0627\u0628\u062a \u0647\u0648 \u0639\u062f\u062f \u063a\u064a\u0631 \u0646\u0633\u0628\u064a<\/p>\n

\"\u0642\u0627\u0646\u0648\u0646<\/a>

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