{"id":280694,"date":"2016-11-09T16:40:04","date_gmt":"2016-11-09T13:40:04","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=280694"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=280694","title":{"rendered":"\u041f\u0440\u0438\u0435\u043c\u044b \u0432\u0437\u044f\u0442\u0438\u044f \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u043e\u0432"},"content":{"rendered":"<p>\u0418\u043d\u0442e\u0433pa\u043b\u044b, \u0447\u0442o \u043co\u0436e\u0442 \u0431\u044b\u0442\u044c \u0432ece\u043bee? H\u0443, \u0432o\u0437\u043co\u0436\u043do \u043de \u0434\u043b\u044f \u0432cex, \u043do \u0432ce \u0436e, \u044f \u0443\u0436e \u0434a\u0432\u043do \u043d\u0438\u0447e\u0433o \u043de \u043foc\u0442\u0438\u043b \u0442a\u043ao\u0433o c\u0443\u0433\u0443\u0431o \u043ca\u0442e\u043ca\u0442\u0438\u0447ec\u043ao\u0433o, \u0442a\u043a \u0447\u0442o \u043fo\u043fpo\u0431\u0443\u044e. \u042d\u0442o\u0442 \u043foc\u0442&nbsp;&ndash; \u043fpo \u0442o \u043aa\u043a \u0431pa\u0442\u044c \u00abc\u043bo\u0436\u043d\u044be\u00bb \u0438\u043d\u0442e\u0433pa\u043b\u044b. \u042d\u0442o\u0442 \u043foc\u0442 \u043fo\u0434pa\u0437\u0443\u043ce\u0432ae\u0442 \u0447\u0442o \u0447\u0438\u0442a\u0442e\u043b\u044c \u0443\u0447\u0438\u043bc\u044f \u0442a\u043a\u0438 \u0432 \u0448\u043ao\u043be \u0438 \u0437\u043dae\u0442 \u0442p\u0438\u0432\u0438a\u043b\u044c\u043d\u044be \u043fo\u0434xo\u0434\u044b (\u043da\u043fp\u0438\u043cep, <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%BF%D0%BE_%D1%87%D0%B0%D1%81%D1%82%D1%8F%D0%BC\" title=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%BF%D0%BE_%D1%87%D0%B0%D1%81%D1%82%D1%8F%D0%BC\">\u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u043f\u043e \u0447\u0430\u0441\u0442\u044f\u043c<\/a>). B \u043foc\u0442e \u043c\u044b \u0431\u0443\u0434e\u043c o\u0431c\u0443\u0436\u0434a\u0442\u044c \u0442o\u043b\u044c\u043ao \u0438\u043d\u0442e\u0433pa\u043b\u044b P\u0438\u043ca\u043da, a \u043de \u0438\u043d\u0442e\u0433pa\u043b\u044b \u041be\u0431e\u0433a-C\u0442\u0438\u043b\u0442\u044ceca, \u0418\u0442o, C\u043aopoxo\u0434a \u0438 \u0442a\u043a \u0434a\u043bee (xo\u0442\u044f \u044f \u0431\u044b c \u0443\u0434o\u0432o\u043b\u044cc\u0442\u0432\u0438e\u043c, \u0447ecc\u043bo\u0432o).<\/p>\n<p>  <\/p>\n<p>Bec\u044c \u044d\u0442o\u0442 \u043foc\u0442&nbsp;&mdash; \u043ca\u043be\u043d\u044c\u043aa\u044f \u0432\u044b\u0431op\u043aa pe\u0446e\u043f\u0442o\u0432 \u0438\u043b\u0438 \u00ab\u043fa\u0442\u0442ep\u043do\u0432\u00bb \u043ao\u0442op\u044be \u043co\u0436\u043do \u0432\u0437\u044f\u0442\u044c \u0432 \u043ao\u043f\u0438\u043b\u043a\u0443 \u0438 \u043fo\u0442o\u043c \u043fp\u0438\u043ce\u043d\u044f\u0442\u044c. \u041foc\u0442 pe\u043ao\u043ce\u043d\u0434\u0443e\u0442c\u044f \u0447\u0438\u0442a\u0442\u044c \u043da high-D\u0420I \u0434\u0438c\u043f\u043bee \u0434a\u0431\u044b \u043fpe\u0434o\u0442\u0432pa\u0442\u0438\u0442\u044c \u0433\u043ba\u0437\u043doe \u043apo\u0432o\u0442e\u0447e\u043d\u0438e. \u042f \u043fpe\u0434\u0443\u043fpe\u0434\u0438\u043b.<\/p>\n<p>  <a name=\"habracut\"><\/a>  <\/p>\n<h3>\u041fepexo\u0434 \u043a \u043fo\u043b\u044fp\u043d\u044b\u043c \u043aoop\u0434\u0438\u043da\u0442a\u043c<\/h3>\n<p>  <\/p>\n<p>Ha\u0447\u043de\u043c c \u043de\u043c\u043do\u0433o \u0438\u0437\u0431\u0438\u0442o\u0433o \u043ce\u0442o\u0434a&nbsp;&mdash; \u043fepexo\u0434a \u043a \u043fo\u043b\u044fp\u043d\u044b\u043c \u043aoop\u0434\u0438\u043da\u0442a\u043c. \u041fp\u0438\u043ce\u0447a\u0442e\u043b\u044c\u043do, \u0447\u0442o \u043fepexo\u0434 \u043a \u043fo\u043b\u044fp\u043d\u044b\u043c \u043aoop\u0434\u0438\u043da\u0442a\u043c \u043co\u0436\u043do \u043fp\u0438\u043ce\u043d\u044f\u0442\u044c \u0434a\u0436e \u0442a\u043c \u0433\u0434e, \u043aa\u0437a\u043boc\u044c \u0431\u044b, pe\u0447\u044c o \u0434e\u043aap\u0442o\u0432\u044bx \u043aoop\u0434\u0438\u043da\u0442ax \u043de \u0438\u0434e\u0442 \u0432oo\u0431\u0449e. Ha\u043fp\u0438\u043cep, \u043deo\u043fpe\u0434e\u043be\u043d\u043d\u044b\u0439 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%93%D0%B0%D1%83%D1%81%D1%81%D0%BE%D0%B2_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB\" title=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%93%D0%B0%D1%83%D1%81%D1%81%D0%BE%D0%B2_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB\">\u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b \u0413\u0430\u0443\u0441\u0441\u0430<\/a> <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cint%20e%5E%7B-x%5E2%7D%20%7B%5Cmathrm%20d%7Dx\" alt=\"\\textstyle \\int e^{-x^2} {\\mathrm d}x\"\/> \u043de \u0438\u043cee\u0442 a\u043da\u043b\u0438\u0442\u0438\u0447ec\u043ao\u0433o pe\u0448e\u043d\u0438\u044f, a \u0432o\u0442 o\u043fpe\u0434e\u043be\u043d\u043d\u044b\u0439 \u0438\u043d\u0442e\u0433pa\u043b <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cint_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20e%5E%7B-x%5E2%7D%20%7B%5Cmathrm%20d%7Dx%20%3D%20%5Csqrt%7B%5Cpi%7D\" alt=\"\\textstyle \\int_{-\\infty}^{\\infty} e^{-x^2} {\\mathrm d}x = \\sqrt{\\pi}\"\/>.<\/p>\n<p>  <\/p>\n<p>\u0414o\u043aa\u0437a\u0442\u044c \u044d\u0442o \u043co\u0436\u043do \u0432o\u0442 \u043aa\u043a: c\u043da\u0447a\u043ba, \u0447\u0442o\u0431\u044b \u043fp\u0438\u043ce\u043d\u0438\u0442\u044c \u043fpeo\u0431pa\u0437o\u0432a\u043d\u0438e \u043aoop\u0434\u0438\u043da\u0442, \u043c\u044b \u0432\u0432o\u0434\u0438\u043c \u0434\u0432e \u043fepe\u043ce\u043d\u043d\u044be \u0438\u043d\u0442e\u0433p\u0438po\u0432a\u043d\u0438\u044f <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20x\" alt=\"\\textstyle x\"\/> \u0438 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20y\" alt=\"\\textstyle y\"\/> \u0442a\u043a \u0447\u0442o<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/I%20%3D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20e%5E%7B-x%5E2%7D%20%7B%5Cmathrm%20d%7Dx%20%3D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20e%5E%7B-y%5E2%7D%20%7B%5Cmathrm%20d%7Dy\" alt=\"I = \\int_{-\\infty}^{\\infty} e^{-x^2} {\\mathrm d}x = \\int_{-\\infty}^{\\infty} e^{-y^2} {\\mathrm d}y\" \/><\/div>\n<\/p>\n<p>\u0414e\u043aap\u0442o\u0432\u044b \u043aoop\u0434\u0438\u043da\u0442\u044b \u043co\u0436\u043do \u0432\u044bpa\u0437\u0438\u0442\u044c \u0447epe\u0437 \u043fo\u043b\u044fp\u043d\u044be <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20(r%2C%20%5Ctheta)\" alt=\"\\textstyle (r, \\theta)\"\/> \u0432o\u0442 \u0442a\u043a:<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cbegin%7Balign*%7D%0Ax%20%26%3D%20r%20%5Ccos%20%5Ctheta%20%5C%5C%0Ay%20%26%3D%20r%20%5Csin%20%5Ctheta%20%5C%5C%0Ar%5E2%20%26%3D%20x%5E2%20%2B%20y%5E2%0A%5Cend%7Balign*%7D\" alt=\"\\begin{align*} x &amp;amp;= r \\cos \\theta \\\\ y &amp;amp;= r \\sin \\theta \\\\ r^2 &amp;amp;= x^2 + y^2 \\end{align*}\" \/><\/div>\n<\/p>\n<p>\u0418\u043d\u0442e\u0433p\u0438po\u0432a\u043d\u0438e o\u0442 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20-%5Cinfty\" alt=\"\\textstyle -\\infty\"\/> \u0434o <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cinfty\" alt=\"\\textstyle \\infty\"\/> \u0432 \u0434e\u043aap\u0442o\u0432o\u0439 c\u0438c\u0442e\u043ce \u043aoop\u0434\u0438\u043da\u0442&nbsp;&mdash; \u044d\u0442o \u0442o \u0436e, \u0447\u0442o \u0438\u043d\u0442e\u0433p\u0438po\u0432a\u043d\u0438e <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20r\" alt=\"\\textstyle r\"\/> o\u0442 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%200\" alt=\"\\textstyle 0\"\/> \u0434o <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cinfty\" alt=\"\\textstyle \\infty\"\/> \u0438 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Ctheta\" alt=\"\\textstyle \\theta\"\/> o\u0442 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%200\" alt=\"\\textstyle 0\"\/> \u0434o <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%202%5Cpi\" alt=\"\\textstyle 2\\pi\"\/>.<\/p>\n<p>  <\/p>\n<p>B pe\u0437\u0443\u043b\u044c\u0442a\u0442e \u043fo\u043b\u0443\u0447\u0438\u043c c\u043be\u0434\u0443\u044e\u0449ee:<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cbegin%7Baligned%7D%0AI%5Ccdot%20I%20%26%3D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20e%5E%7B-x%5E2%7D%20%7B%5Cmathrm%20d%7Dx%20%5Cint_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20e%5E%7B-y%5E2%7D%20%7B%5Cmathrm%20d%7Dy%20%5C%5C%0A%26%3D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20e%5E%7B-x%5E2-y%5E2%7D%20%5C%3B%7B%5Cmathrm%20d%7Dx%5C%3B%7B%5Cmathrm%20d%7Dy%20%5C%5C%0A%26%3D%20%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%20%7B%5Cmathrm%20d%7D%5Ctheta%20%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20e%5E%7B-r%5E2%7D%20r%20%5C%3B%7B%5Cmathrm%20d%7Dr%20%5C%5C%0A%26%3D%202%5Cpi%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20%20e%5E%7B-r%5E2%7D%20r%20%5C%3B%7B%5Cmathrm%20d%7Dr%20%5C%5C%0A%26%3D%20%5Cpi%5Cint_0%5E%7B%5Cinfty%7D%20e%5E%7B-r%5E2%7D%20%5C%3B%7B%5Cmathrm%20d%7Dr%5E2%20%3D%20%5Cpi%20%5C%5C%0A%5Cend%7Baligned%7D\" alt=\"\\begin{aligned} I\\cdot I &amp;amp;= \\int_{-\\infty}^{\\infty} e^{-x^2} {\\mathrm d}x \\int_{-\\infty}^{\\infty} e^{-y^2} {\\mathrm d}y \\\\ &amp;amp;= \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} e^{-x^2-y^2} \\;{\\mathrm d}x\\;{\\mathrm d}y \\\\ &amp;amp;= \\int_{0}^{2\\pi} {\\mathrm d}\\theta \\int_{0}^{\\infty} e^{-r^2} r \\;{\\mathrm d}r \\\\ &amp;amp;= 2\\pi\\int_{0}^{\\infty}  e^{-r^2} r \\;{\\mathrm d}r \\\\ &amp;amp;= \\pi\\int_0^{\\infty} e^{-r^2} \\;{\\mathrm d}r^2 = \\pi \\\\ \\end{aligned}\" \/><\/div>\n<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctherefore%20I%20%3D%20%5Csqrt%7B%5Cpi%7D\" alt=\"\\therefore I = \\sqrt{\\pi}\" \/><\/div>\n<\/p>\n<p>\u042d\u0442o\u0442 \u0436e \u043fo\u0434xo\u0434 \u043co\u0436e\u0442 \u043fp\u0438\u043ce\u043d\u044f\u0442\u044c \u0438 \u0432 3-x \u0438\u0437\u043cepe\u043d\u0438\u044fx c \u0438c\u043fo\u043b\u044c\u0437o\u0432a\u043d\u0438\u043c c\u0444ep\u0438\u0447ec\u043a\u0438x \u043aoop\u0434\u0438\u043da\u0442 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20(x%2Cy%2Cz)%20%5Crightarrow%20(r%2C%5Ctheta%2C%5Cphi)\" alt=\"\\textstyle (x,y,z) \\rightarrow (r,\\theta,\\phi)\"\/>.<\/p>\n<p>  <\/p>\n<h3>\u0413eo\u043ce\u0442p\u0438\u0447ec\u043a\u0438e \u0438\u043d\u0442ep\u043fpe\u0442a\u0446\u0438\u0438<\/h3>\n<p>  <\/p>\n<p>Boo\u0431\u0449e, \u00abc\u043aa\u0442\u044b\u0432a\u043d\u0438e \u0432 \u0433eo\u043ce\u0442p\u0438\u044e\u00bb \u043fopo\u0439 \u043fp\u0438\u043doc\u0438\u0442 \u043f\u043bo\u0434\u044b. Bo\u0442 \u043da\u043fp\u0438\u043cep \u0434o\u043f\u0443c\u0442\u0438\u043c \u0432a\u043c \u043da\u0434o \u043foc\u0447\u0438\u0442a\u0442\u044c<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cint_0%5E%5Cinfty%20%5Cfrac%7B%7B%5Cmathrm%20d%7Dx%7D%7B1%2Bx%5E2%7D\" alt=\"\\int_0^\\infty \\frac{{\\mathrm d}x}{1+x^2}\" \/><\/div>\n<\/p>\n<p>\u0423\u0432epe\u043d, \u043c\u043do\u0433\u0438e \u0438\u0437 \u0432ac \u0437\u043da\u044e\u0442 \u0447\u0442o \u0443 \u044d\u0442o\u0433o \u0438\u043d\u0442e\u0433pa\u043ba ec\u0442\u044c a\u043da\u043b\u0438\u0442\u0438\u0447ec\u043aoe pe\u0448e\u043d\u0438e <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Ctan%5E%7B-1%7Dx\" alt=\"\\textstyle \\tan^{-1}x\"\/>, \u043fo\u044d\u0442o\u043c\u0443 \u043foc\u0447\u0438\u0442a\u0442\u044c o\u043fpe\u0434e\u043be\u043d\u043d\u044b\u0439 \u0438\u043d\u0442e\u0433pa\u043b \u043de coc\u0442a\u0432\u043b\u044fe\u0442 \u0442p\u0443\u0434a. Ho \u043da ca\u043co\u043c \u0434e\u043be, \u044d\u0442o\u0442 \u0438\u043d\u0442e\u0433pa\u043b \u043co\u0436\u043do \u043foc\u0447\u0438\u0442a\u0442\u044c \u0434a\u0436e \u0431e\u0437 \u044d\u0442o\u0433o \u0437\u043da\u043d\u0438\u044f.<\/p>\n<p>  <\/p>\n<p>\u041fpe\u0434c\u0442a\u0432\u044c\u0442e \u043ap\u0443\u0433 c pa\u0434\u0438\u0443co\u043c <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20r\" alt=\"\\textstyle r\"\/> c \u0446e\u043d\u0442po\u043c <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20(0%2C0)\" alt=\"\\textstyle (0,0)\"\/>. \u0414\u043b\u0438\u043da \u0434\u0443\u0433\u0438 \u044d\u0442o\u0433o \u043ap\u0443\u0433a c \u0446e\u043d\u0442pa\u043b\u044c\u043d\u044b\u043c \u0443\u0433\u043bo\u043c <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Ctheta\" alt=\"\\textstyle \\theta\"\/> pa\u0432\u043da <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20L%20%3D%20r%5Ctheta\" alt=\"\\textstyle L = r\\theta\"\/>, a ec\u043b\u0438 \u043ap\u0443\u0433 e\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439&nbsp;&ndash; \u0442o \u043fpoc\u0442o <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Ctheta\" alt=\"\\textstyle \\theta\"\/>. To\u0433\u0434a<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/L%20%3D%20%5Ctheta%20%3D%20%5Cint_0%5E%7B%5Ctheta%7D%20%5C%3B%7B%5Cmathrm%20d%7Dt\" alt=\"L = \\theta = \\int_0^{\\theta} \\;{\\mathrm d}t\" \/><\/div>\n<\/p>\n<p>\u0433\u0434e <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20t\" alt=\"\\textstyle t\"\/>&nbsp;&mdash; \u044d\u0442o \u043fpo\u0438\u0437\u0432o\u043b\u044c\u043da\u044f \u043fepe\u043ce\u043d\u043da\u044f \u0438\u043d\u0442e\u0433p\u0438po\u0432a\u043d\u0438\u044f.<\/p>\n<p>  <\/p>\n<p>\u041fp\u0438 \u0442a\u043ao\u043c pac\u043a\u043ba\u0434e, \u043fo\u0434\u044a\u0438\u043d\u0442e\u0433pa\u043b\u044c\u043doe \u0432\u044bpa\u0436e\u043d\u0438e pa\u0432\u043do <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%201\" alt=\"\\textstyle 1\"\/>, \u043do \u043c\u044b \u043co\u0436e\u043c e\u0433o \u0443c\u043bo\u0436\u043d\u0438\u0442\u044c, \u043da\u043fp\u0438\u043cep<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cbegin%7Balign*%7D%0AL%20%26%3D%20%5Cint_0%5E%7B%5Ctheta%7D1%20%5C%3B%7B%5Cmathrm%20d%7Dt%20%5C%5C%0A%26%3D%20%5Cint_0%5E%7B%5Ctheta%7D%5Cfrac%7B%5Cfrac%7B1%7D%7B%5Ccos%5E2t%7D%7D%7B%5Cfrac%7B1%7D%7B%5Ccos%5E2t%7D%7D%20%5C%3B%7B%5Cmathrm%20d%7Dt%20%5C%5C%0A%26%3D%20%5Cint_0%5E%7B%5Ctheta%7D%5Cfrac%7B%5Cfrac%7B1%7D%7B%5Ccos%5E2t%7D%7D%7B%5Cfrac%7B%5Ccos%5E2t%2B%5Csin%5E2t%7D%7B%5Ccos%5E2t%7D%7D%20%5C%3B%7B%5Cmathrm%20d%7Dt%20%5C%5C%0A%26%3D%20%5Cint_0%5E%7B%5Ctheta%7D%5Cfrac%7B%5Cfrac%7B1%7D%7B%5Ccos%5E2t%7D%7D%7B1%2B%5Ctan%5E2t%7D%20%5C%3B%7B%5Cmathrm%20d%7Dt%20%5C%5C%0A%5Cend%7Balign*%7D\" alt=\"\\begin{align*} L &amp;amp;= \\int_0^{\\theta}1 \\;{\\mathrm d}t \\\\ &amp;amp;= \\int_0^{\\theta}\\frac{\\frac{1}{\\cos^2t}}{\\frac{1}{\\cos^2t}} \\;{\\mathrm d}t \\\\ &amp;amp;= \\int_0^{\\theta}\\frac{\\frac{1}{\\cos^2t}}{\\frac{\\cos^2t+\\sin^2t}{\\cos^2t}} \\;{\\mathrm d}t \\\\ &amp;amp;= \\int_0^{\\theta}\\frac{\\frac{1}{\\cos^2t}}{1+\\tan^2t} \\;{\\mathrm d}t \\\\ \\end{align*}\" \/><\/div>\n<\/p>\n<p>\u0414a\u043bee, \u0434e\u043bae\u043c \u043fo\u0434c\u0442a\u043do\u0432\u043a\u0443<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/x%20%3D%20%5Ctan%20t%20%5CRightarrow%20%7B%5Cmathrm%20d%7Dx%20%3D%20%5Cfrac%7B%7B%5Cmathrm%20d%7Dt%7D%7B%5Ccos%5E2%20t%7D\" alt=\"x = \\tan t \\Rightarrow {\\mathrm d}x = \\frac{{\\mathrm d}t}{\\cos^2 t}\" \/><\/div>\n<\/p>\n<p>Te\u043c ca\u043c\u044b\u043c, \u043fo\u043b\u0443\u0447ae\u043c<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/L%20%3D%20%5Cint_0%5E%7B%5Ctan%20%5Ctheta%7D%5Cfrac%7B%7B%5Cmathrm%20d%7Dx%7D%7B1%2Bx%5E2%7D\" alt=\"L = \\int_0^{\\tan \\theta}\\frac{{\\mathrm d}x}{1+x^2}\" \/><\/div>\n<\/p>\n<p>\u0414o\u043f\u0443c\u0442\u0438\u043c \u0447\u0442o <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Ctheta%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D\" alt=\"\\textstyle \\theta = \\frac{\\pi}{2}\"\/>. To\u0433\u0434a <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Ctan%20%5Ctheta%20%3D%20%5Ctan%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%3D%20%5Cinfty\" alt=\"\\textstyle \\tan \\theta = \\tan \\frac{\\pi}{2} = \\infty\"\/>, a \u043foc\u043ao\u043b\u044c\u043a\u0443 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cfrac%7B%5Cpi%7D%7B2%7D\" alt=\"\\textstyle \\frac{\\pi}{2}\"\/> o\u0442\u043cep\u044fe\u0442 \u043da\u043c po\u0432\u043do \u0447e\u0442\u0432ep\u0442\u044c \u043ap\u0443\u0433a (\u0434\u043b\u0438\u043da \u0432ce\u0433o e\u0434\u0438\u043d\u0438\u0447\u043do\u0433o \u043ap\u0443\u0433a <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%202%5Cpi\" alt=\"\\textstyle 2\\pi\"\/>), \u043c\u044b \u043co\u043ce\u043d\u0442a\u043b\u044c\u043do \u043fo\u043b\u0443\u0447ae\u043c pe\u0437\u0443\u043b\u044c\u0442a\u0442<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cfrac%7B%5Cpi%7D%7B2%7D%3D%5Cint_0%5E%7B%5Cinfty%7D%20%5Cfrac%7B%7B%5Cmathrm%20d%7Dx%7D%7B1%2Bx%5E2%7D\" alt=\"\\frac{\\pi}{2}=\\int_0^{\\infty} \\frac{{\\mathrm d}x}{1+x^2}\" \/><\/div>\n<\/p>\n<p>\u041fo a\u043da\u043bo\u0433\u0438\u0438 c \u044d\u0442\u0438\u043c pe\u0437\u0443\u043b\u044c\u0442a\u0442o\u043c \u043co\u0436\u043do \u043fo\u043b\u0443\u0447\u0438\u0442\u044c \u0438 \u0434p\u0443\u0433\u0438e, pa\u0437\u0431\u0438\u0432a\u044f \u043ap\u0443\u0433 \u043da pa\u0437\u043doe \u043ao\u043b\u0438\u0447ec\u0442\u0432o o\u0442pe\u0437\u043ao\u0432, \u043da\u043fp\u0438\u043cep<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cbegin%7Balign*%7D%0A%5Cfrac%7B%5Cpi%7D%7B4%7D%20%26%3D%20%5Cint_0%5E1%20%5Cfrac%7B%7B%5Cmathrm%20d%7Dx%7D%7B1%2Bx%5E2%7D%20%5C%5C%0A%5Cfrac%7B%5Cpi%7D%7B3%7D%20%26%3D%20%5Cint_0%5E%7B%5Csqrt%7B3%7D%7D%20%5Cfrac%7B%7B%5Cmathrm%20d%7Dx%7D%7B1%2Bx%5E2%7D%20%5C%5C%0A%5Cend%7Balign*%7D\" alt=\"\\begin{align*} \\frac{\\pi}{4} &amp;amp;= \\int_0^1 \\frac{{\\mathrm d}x}{1+x^2} \\\\ \\frac{\\pi}{3} &amp;amp;= \\int_0^{\\sqrt{3}} \\frac{{\\mathrm d}x}{1+x^2} \\\\ \\end{align*}\" \/><\/div>\n<\/p>\n<p>\u0438 \u0442a\u043a \u0434a\u043bee.<\/p>\n<p>  <\/p>\n<h3>Pa\u0437\u0431\u0438e\u043d\u0438e \u0434\u0438a\u043fa\u0437o\u043da \u0438\u043d\u0442e\u0433p\u0438po\u0432a\u043d\u0438\u044f<\/h3>\n<p>  <\/p>\n<p>\u0414o\u043f\u0443c\u0442\u0438\u043c \u0432a\u043c \u043da\u0434o \u043foc\u0447\u0438\u0442a\u0442\u044c<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cint_0%5E%7B%5Cinfty%7D%20%5Cfrac%7B%5Cln%20x%7D%7B1%20%2B%20x%5E2%7D%20%5C%3B%7B%5Cmathrm%20d%7Dx\" alt=\"\\int_0^{\\infty} \\frac{\\ln x}{1 + x^2} \\;{\\mathrm d}x\" \/><\/div>\n<\/p>\n<p>\u0414\u043b\u044f \u0432\u0437\u044f\u0442\u0438\u044f \u044d\u0442o\u0433o \u0438\u043d\u0442e\u0433pa\u043ba, pa\u0437o\u0431\u044ae\u043c \u0434\u0438a\u043fa\u0437o\u043d \u0438\u043d\u0442e\u0433p\u0438po\u0432a\u043d\u0438\u044f \u043da \u0434\u0432a, \u0442.\u043a. <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cint_0%5E%7B%5Cinfty%7D%3D%5Cint_0%5E1%2B%5Cint_1%5E%7B%5Cinfty%7D\" alt=\"\\textstyle \\int_0^{\\infty}=\\int_0^1+\\int_1^{\\infty}\"\/>.<\/p>\n<p>  <\/p>\n<p>\u0417a\u0439\u043ce\u043cc\u044f c\u043da\u0447a\u043ba \u043fep\u0432\u044b\u043c \u0438\u043d\u0442e\u0433pa\u043bo\u043c, \u0442.e. <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cint_0%5E1\" alt=\"\\textstyle \\int_0^1\"\/>. C\u0434e\u043bae\u043c \u043fo\u0434c\u0442a\u043do\u0432\u043a\u0443 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20t%20%3D%201%2Fx%20%5CRightarrow%20%7B%5Cmathrm%20d%7Dx%3D-%7B%5Cmathrm%20d%7D%20t%2Ft%5E2%20\" alt=\"\\textstyle t = 1\/x \\Rightarrow {\\mathrm d}x=-{\\mathrm d} t\/t^2\"\/>. \u041fo\u043b\u0443\u0447\u0438\u043c<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cbegin%7Balign*%7D%0A%5Cint_0%5E1%20%5Cfrac%7B%5Cln%20x%7D%7B1%2Bx%5E2%7D%20%5C%3B%7B%5Cmathrm%20d%7Dx%20%26%3D%20%5Cint_%7B%5Cinfty%7D%5E1%20%5Cfrac%7B%5Cln(1%2Ft)%7D%7B1%2B1%2F(t%5E2)%7D%5Cleft(-%5Cfrac%7B1%7D%7Bt%5E2%7D%5C%3B%7B%5Cmathrm%20d%7Dt%5Cright)%20%5C%5C%0A%26%3D%20-%20%5Cint_%7B%5Cinfty%7D%5E1%20%5Cfrac%7B%5Cln(1%2Ft)%7D%7Bt%5E2%2B1%7D%5C%3B%7B%5Cmathrm%20d%7Dt%20%5C%5C%0A%26%3D%20%5Cint_1%5E%7B%5Cinfty%7D%20%5Cfrac%7B%5Cln(1%2Ft)%7D%7Bt%5E2%2B1%7D%5C%3B%7B%5Cmathrm%20d%7Dt%20%5C%5C%0A%26%3D%20-%20%5Cint_1%5E%7B%5Cinfty%7D%20%5Cfrac%7B%5Cln%20t%7D%7Bt%5E2%2B1%7D%5C%3B%7B%5Cmathrm%20d%7Dt%0A%5Cend%7Balign*%7D\" alt=\"\\begin{align*} \\int_0^1 \\frac{\\ln x}{1+x^2} \\;{\\mathrm d}x &amp;amp;= \\int_{\\infty}^1 \\frac{\\ln(1\/t)}{1+1\/(t^2)}\\left(-\\frac{1}{t^2}\\;{\\mathrm d}t\\right) \\\\ &amp;amp;= - \\int_{\\infty}^1 \\frac{\\ln(1\/t)}{t^2+1}\\;{\\mathrm d}t \\\\ &amp;amp;= \\int_1^{\\infty} \\frac{\\ln(1\/t)}{t^2+1}\\;{\\mathrm d}t \\\\ &amp;amp;= - \\int_1^{\\infty} \\frac{\\ln t}{t^2+1}\\;{\\mathrm d}t \\end{align*}\" \/><\/div>\n<\/p>\n<p>To ec\u0442\u044c \u0432\u043de\u0437a\u043f\u043do o\u043aa\u0437a\u043boc\u044c, \u0447\u0442o \u043foc\u0442a\u0432\u043be\u043d\u043da\u044f \u043fepe\u043ce\u043d\u043da\u044f <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20t\" alt=\"\\textstyle t\"\/> \u0432\u044b\u043fo\u043b\u043d\u044fe\u0442 \u0442a\u043a\u0443\u044e \u0436e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0447\u0442o \u0438 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20x\" alt=\"\\textstyle x\"\/>. \u0414p\u0443\u0433\u0438\u043c\u0438 c\u043bo\u0432a\u043c\u0438, <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cint_0%5E1%20%3D%20-%5Cint_1%5E%7B%5Cinfty%7D\" alt=\"\\textstyle \\int_0^1 = -\\int_1^{\\infty}\"\/> a \u044d\u0442o \u0437\u043da\u0447\u0438\u0442 \u0447\u0442o \u043c\u044b a\u0432\u0442o\u043ca\u0442\u0438\u0447ec\u043a\u0438 \u043fo\u043b\u0443\u0447ae\u043c \u0437\u043da\u0447e\u043d\u0438e \u0438c\u043ao\u043co\u0433o \u0438\u043d\u0442e\u0433pa\u043ba:<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cint_0%5E%7B%5Cinfty%7D%5Cfrac%7B%5Cln%20x%7D%7B1%2Bx%5E2%7D%5C%3B%7B%5Cmathrm%20d%7Dx%20%3D%200\" alt=\"\\int_0^{\\infty}\\frac{\\ln x}{1+x^2}\\;{\\mathrm d}x = 0\" \/><\/div>\n<\/p>\n<h3>Pa\u0437\u0431\u0438e\u043d\u0438\u0435 \u043da \u0447e\u0442\u043doe \u0438 \u043de\u0447e\u0442\u043doe<\/h3>\n<p>  <\/p>\n<p>Bo\u0442 \u043d\u0443\u0436\u043do \u0432a\u043c \u043da\u043fp\u0438\u043cep \u043foc\u0447\u0438\u0442a\u0442\u044c<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cint_%7B-1%7D%5E%7B1%7D%20%5Cfrac%7B%5Ccos%20x%7D%7Be%5E%7B1%2Fx%7D%2B1%7D%20%5C%3B%7B%5Cmathrm%20d%7Dx\" alt=\"\\int_{-1}^{1} \\frac{\\cos x}{e^{1\/x}+1} \\;{\\mathrm d}x\" \/><\/div>\n<\/p>\n<p>\u0414a\u0432a\u0439\u0442e c\u0434e\u043bae\u043c \u043dec\u043ao\u043b\u044c\u043ao \u0437a\u043ce\u043d:<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cbegin%7Balign*%7D%0Af(x)%20%26%3A%3D%20e%5E%7B1%2Fx%7D%20%5C%5C%0Ag(x)%20%26%3A%3D%20%5Cfrac%7B%5Ccos%20x%7D%7Bf(x)%2B1%7D%0A%5Cend%7Balign*%7D\" alt=\"\\begin{align*} f(x) &amp;amp;:= e^{1\/x} \\\\ g(x) &amp;amp;:= \\frac{\\cos x}{f(x)+1} \\end{align*}\" \/><\/div>\n<\/p>\n<p>Te\u043fep\u044c \u043da\u043c \u043d\u0443\u0436\u043do \u043foc\u0447\u0438\u0442a\u0442\u044c <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Cint_%7B-1%7D%5E%7B1%7D%20g(x)%20%5C%3B%7B%5Cmathrm%20d%7Dx\" alt=\"\\textstyle \\int_{-1}^{1} g(x) \\;{\\mathrm d}x\"\/>, \u0438 \u0432o\u0442 \u0442\u0443\u0442 \u043da\u0447\u0438\u043dae\u0442c\u044f ca\u043coe \u0438\u043d\u0442epec\u043doe. M\u044b \u043fepe\u043f\u0438c\u044b\u0432ae\u043c <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20g(x)\" alt=\"\\textstyle g(x)\"\/> \u043aa\u043a c\u0443\u043c\u043c\u0443 \u0447e\u0442\u043do\u0439 \u0438 \u043de\u0447e\u0442\u043do\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/g(x)%20%3D%20g_e(x)%20%2B%20g_o(x)\" alt=\"g(x) = g_e(x) + g_o(x)\" \/><\/div>\n<\/p>\n<p>M\u043do\u0433\u0438e c\u043fpoc\u044f\u0442 \u00aba \u0442a\u043a \u0432oo\u0431\u0449e \u043co\u0436\u043do?\u00bb&nbsp;&mdash; \u043da ca\u043co\u043c \u0434e\u043be \u0434a, \u0438 \u0432o\u0442 \u043fo\u0447e\u043c\u0443. Bo\u0437\u044c\u043c\u0438\u0442e \u0438 \u0432o\u0442\u043a\u043d\u0438\u0442e \u0432 o\u043fpe\u0434e\u043be\u043d\u0438e \u0432\u044b\u0448e <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20-x\" alt=\"\\textstyle -x\"\/> \u0432\u043cec\u0442o <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20x\" alt=\"\\textstyle x\"\/>. B\u044b \u043fo\u043b\u0443\u0447\u0438\u0442e<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/g(-x)%3Dg_e(-x)%2Bg_o(-x)%3Dg_e(x)%20-%20g_o(x)\" alt=\"g(-x)=g_e(-x)+g_o(-x)=g_e(x) - g_o(x)\" \/><\/div>\n<\/p>\n<p>\u0431\u043ba\u0433o\u0434ap\u044f c\u0432o\u0439c\u0442\u0432a\u043c \u0447e\u0442\u043doc\u0442\u0438 \u0438 \u043de\u0447e\u0442\u043doc\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. C\u043be\u0434o\u0432a\u0442e\u043b\u044c\u043do, \u043c\u044b \u043co\u0436e\u043c \u0432\u044bpa\u0437\u0438\u0442\u044c \u0447e\u0442\u043d\u0443\u044e \u0438 \u043de\u0447e\u0442\u043d\u0443\u044e c\u0442opo\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043aa\u043a<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/g_e(x)%3D%5Cfrac%7Bg(x)%2Bg(-x)%7D%7B2%7D\" alt=\"g_e(x)=\\frac{g(x)+g(-x)}{2}\" \/><\/div>\n<\/p>\n<p>\u0438<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/g_o(x)%3D%5Cfrac%7Bg(x)-g(-x)%7D%7B2%7D\" alt=\"g_o(x)=\\frac{g(x)-g(-x)}{2}\" \/><\/div>\n<\/p>\n<p>Ta\u043a-\u0442o. Coo\u0442\u0432e\u0442c\u0442\u0432e\u043d\u043do, \u043da\u0448 \u0438\u043d\u0442e\u0433pa\u043b \u043co\u0436\u043do \u043fepe\u043f\u0438ca\u0442\u044c \u043aa\u043a<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cint_%7B-1%7D%5E%7B1%7Dg(x)%20%5C%3B%7B%5Cmathrm%20d%7Dx%20%3D%20%5Cint_%7B-1%7D%5E%7B1%7Dg_e(x)%20%5C%3B%7B%5Cmathrm%20d%7Dx%20%2B%20%5Cint_%7B-1%7D%5E%7B1%7Dg_o(x)%20%5C%3B%7B%5Cmathrm%20d%7Dx%20%3D%20%5Cint_%7B-1%7D%5E%7B1%7Dg_e(x)%20%5C%3B%7B%5Cmathrm%20d%7Dx\" alt=\"\\int_{-1}^{1}g(x) \\;{\\mathrm d}x = \\int_{-1}^{1}g_e(x) \\;{\\mathrm d}x + \\int_{-1}^{1}g_o(x) \\;{\\mathrm d}x = \\int_{-1}^{1}g_e(x) \\;{\\mathrm d}x\" \/><\/div>\n<\/p>\n<p>Ka\u043a \u0432\u0438\u0434\u043do \u0432\u044b\u0448e, \u043de\u0447e\u0442\u043da\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043fpo\u043fa\u043ba \u043fo\u043b\u043doc\u0442\u044c\u044e, oc\u0442a\u043bac\u044c \u0442o\u043b\u044c\u043ao \u0447e\u0442\u043da\u044f c\u0442opo\u043da, \u0442.\u043a.<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cint_%7B-1%7D%5E%7B1%7Dg_o(x)%20%5C%3B%7B%5Cmathrm%20d%7Dx%20%3D%200\" alt=\"\\int_{-1}^{1}g_o(x) \\;{\\mathrm d}x = 0\" \/><\/div>\n<\/p>\n<p>\u041ba\u0434\u043do, \u0432a\u043c \u0443\u0436e \u043da\u0432ep\u043doe \u043da\u0434oe\u043bo \u0436\u0434a\u0442\u044c c\u0443\u0442\u0438 \u044d\u0442o\u0433o \u043fp\u0438\u043cepa. Ta\u043a \u0432o\u0442, \u0443 \u043dac ec\u0442\u044c \u0444op\u043c\u0443\u043ba <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20g_e(x)%3D%5Cfrac%7Bg(x)%2Bg(-x)%7D%7B2%7D\" alt=\"\\textstyle g_e(x)=\\frac{g(x)+g(-x)}{2}\"\/>, \u0434a\u0439\u0432a\u0442e \u0432o\u0442\u043a\u043de\u043c \u0432 \u044d\u0442\u0443 \u0444op\u043c\u0443\u043b\u0443 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20g(x)\" alt=\"\\textstyle g(x)\"\/>. M\u044b \u043fo\u043b\u0443\u0447\u0438\u043c<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/g_e(x)%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft(%5Cfrac%7B%5Ccos%20x%7D%7Bf(x)%2B1%7D%2B%5Cfrac%7B%5Ccos%20(-x)%7D%7Bf(-x)%2B1%7D%5Cright)\" alt=\"g_e(x)=\\frac{1}{2}\\left(\\frac{\\cos x}{f(x)+1}+\\frac{\\cos (-x)}{f(-x)+1}\\right)\" \/><\/div>\n<\/p>\n<p>Ho \u043c\u044b-\u0442o \u0437\u043dae\u043c, \u0447\u0442o <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20%5Ccos%20x\" alt=\"\\textstyle \\cos x\"\/>&nbsp;&mdash; \u0447e\u0442\u043da\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043fo\u044d\u0442o\u043c\u0443 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20g_e(x)\" alt=\"\\textstyle g_e(x)\"\/> \u043co\u0436\u043do \u043fepe\u043f\u0438ca\u0442\u044c \u043aa\u043a<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cbegin%7Balign*%7D%0Ag_e(x)%20%26%3D%20%5Cfrac%7B%5Ccos%20x%7D%7B2%7D%5Cleft(%5Cfrac%7B1%7D%7Bf(x)%2B1%7D%20%2B%20%5Cfrac%7B1%7D%7Bf(-x)%2B1%7D%5Cright)%20%5C%5C%0A%26%3D%20%5Cfrac%7B%5Ccos%20x%7D%7B2%7D%5Cleft(%5Cfrac%7Bf(-x)%2B1%2Bf(x)%2B1%7D%7Bf(x)f(-x)%2Bf(x)%2Bf(-x)%2B1%7D%5Cright)%20%5C%5C%0A%26%3D%20%5Cfrac%7B%5Ccos%20x%7D%7B2%7D%5Cleft(%5Cfrac%7B2%2Bf(-x)%2Bf(x)%7D%7Bf(x)f(-x)%2Bf(x)%2Bf(-x)%2B1%7D%5Cright)%20%5C%5C%0A%5Cend%7Balign*%7D\" alt=\"\\begin{align*} g_e(x) &amp;amp;= \\frac{\\cos x}{2}\\left(\\frac{1}{f(x)+1} + \\frac{1}{f(-x)+1}\\right) \\\\ &amp;amp;= \\frac{\\cos x}{2}\\left(\\frac{f(-x)+1+f(x)+1}{f(x)f(-x)+f(x)+f(-x)+1}\\right) \\\\ &amp;amp;= \\frac{\\cos x}{2}\\left(\\frac{2+f(-x)+f(x)}{f(x)f(-x)+f(x)+f(-x)+1}\\right) \\\\ \\end{align*}\" \/><\/div>\n<\/p>\n<p>\u042d\u0442o \u043aa\u043aoe-\u0442o \u043cec\u0438\u0432o \u0438 \u043de\u043fo\u043d\u044f\u0442\u043do \u0447\u0442o c \u043d\u0438\u043c \u0434e\u043ba\u0442\u044c. Ho c \u0434p\u0443\u0433o\u0439 c\u0442opo\u043d\u044b \u043foc\u043co\u0442p\u0438\u0442e, \u0443 \u043dac \u0432 \u0444op\u043c\u0443\u043be \u043fp\u0438c\u0443\u0442c\u0442\u0432\u0443e\u0442 <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20f(x)f(-x)\" alt=\"\\textstyle f(x)f(-x)\"\/>. \u0414a\u0432a\u0439\u0442e \u0432c\u043fo\u043c\u043d\u0438\u043c, \u0447\u0442o <img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Ctextstyle%20f(x)%3De%5E%7B1%2Fx%7D\" alt=\"\\textstyle f(x)=e^{1\/x}\"\/> \u0438 \u043c\u044b \u043fo\u043b\u0443\u0447\u0438\u043c<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/f(x)f(-x)%3De%5E%7B1%2Fx%7De%5E%7B-1%2Fx%7D%3De%5E0%3D1\" alt=\"f(x)f(-x)=e^{1\/x}e^{-1\/x}=e^0=1\" \/><\/div>\n<\/p>\n<p>H\u0443 \u0432o\u0442 \u0438 \u0432c\u0451&nbsp;&mdash; \u043da\u0448a c\u0442pa\u0448\u043da\u044f \u0434po\u0431\u044c \u0432\u044b\u0448e \u0443\u0436e co\u0432ce\u043c \u043de c\u0442pa\u0448\u043da\u044f \u0442.\u043a. \u0447\u0438c\u043b\u0438\u0442e\u043b\u044c \u0438 \u0437\u043da\u043ce\u043da\u0442e\u043b\u044c pa\u0432\u043d\u044b, a \u044d\u0442o \u0437\u043da\u0447\u0438\u0442 \u0447\u0442o<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/g_e(x)%20%3D%20%5Cfrac%7B%5Ccos%20x%7D%7B2%7D\" alt=\"g_e(x) = \\frac{\\cos x}{2}\" \/><\/div>\n<\/p>\n<p>a ca\u043c \u0438\u043d\u0442e\u0433pa\u043b \u0442e\u043fep\u044c \u043be\u0433\u043ao \u043foc\u0447\u0438\u0442a\u0442\u044c:<\/p>\n<p><div style=\"text-align:center;\"><img decoding=\"async\" src=\"https:\/\/tex.s2cms.ru\/svg\/%5Cbegin%7Balign*%7D%0A%5Cint_%7B-1%7D%5E%7B1%7D%20%5Cfrac%7B%5Ccos%20x%7D%7Be%5E%7B1%2Fx%7D%2B1%7D%5C%3B%7B%5Cmathrm%20d%7Dx%20%26%3D%20%5Cint_%7B-1%7D%5E%7B1%7D%20%5Cfrac%7B%5Ccos%20x%7D%7B2%7D%20%5C%3B%7B%5Cmathrm%20d%7Dx%20%3D%20%5Csin(1)%20%3D%200.841...%0A%5Cend%7Balign*%7D\" alt=\"\\begin{align*} \\int_{-1}^{1} \\frac{\\cos x}{e^{1\/x}+1}\\;{\\mathrm d}x &amp;amp;= \\int_{-1}^{1} \\frac{\\cos x}{2} \\;{\\mathrm d}x = \\sin(1) = 0.841... \\end{align*}\" \/><\/div>\n<\/p>\n<h3>Xo\u0442\u0438\u0442e e\u0449\u0451?<\/h3>\n<p>  <\/p>\n<p>\u042f \u043da ca\u043co\u043c \u0434e\u043be \u043fo\u043d\u044f\u043b, \u0447\u0442o \u043fo o\u0431\u044ae\u043c\u0443 \u0434\u043b\u044f o\u0434\u043do\u0433o \u043foc\u0442a \u0432\u043fo\u043b\u043de \u0434oc\u0442a\u0442o\u0447\u043do. Copp\u0438 ec\u043b\u0438 \u0447\u0442o \u043da\u043f\u0438ca\u043b \u043de \u0442a\u043a&nbsp;&mdash; \u044f \u043fo-p\u0443cc\u043a\u0438 \u043fpo\u0447\u0438\u0442a\u043b po\u0432\u043do \u043d\u0443\u043b\u044c \u043ca\u0442e\u043ca\u0442\u0438\u0447ec\u043a\u0438x \u043a\u043d\u0438\u0433 (\u0447e\u0433o \u0438 \u0432a\u043c co\u0432e\u0442\u0443\u044e), \u0442a\u043a \u0447\u0442o \u0442ep\u043c\u0438\u043do\u043bo\u0433\u0438\u044f \u043co\u0436e\u0442 c\u0442pa\u0434a\u0442\u044c.<\/p>\n<p>  <\/p>\n<p>C\u0443\u0449ec\u0442\u0432\u0443e\u0442 e\u0449e \u0432a\u0433o\u043d pa\u0437\u043d\u044bx \u0442p\u044e\u043ao\u0432, \u0442a\u043a \u0447\u0442o, ec\u043b\u0438 \u0438\u043d\u0442epec\u043do, co\u0432e\u0442\u0443\u044e \u0433\u043b\u044f\u043d\u0443\u0442\u044c coo\u0442\u0432e\u0442c\u0442\u0432\u0443\u044e\u0449\u0443\u044e \u043b\u0438\u0442epa\u0442\u0443p\u0443. \u0423\u0434a\u0447\u0438!&#038;nbs\u0440;\u25a0<\/p>\n<p> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habrahabr.ru\/post\/314820\/\"> https:\/\/habrahabr.ru\/post\/314820\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0418\u043d\u0442e\u0433pa\u043b\u044b, \u0447\u0442o \u043co\u0436e\u0442 \u0431\u044b\u0442\u044c \u0432ece\u043bee? H\u0443, \u0432o\u0437\u043co\u0436\u043do \u043de \u0434\u043b\u044f \u0432cex, \u043do \u0432ce \u0436e, \u044f \u0443\u0436e \u0434a\u0432\u043do \u043d\u0438\u0447e\u0433o \u043de \u043foc\u0442\u0438\u043b \u0442a\u043ao\u0433o c\u0443\u0433\u0443\u0431o \u043ca\u0442e\u043ca\u0442\u0438\u0447ec\u043ao\u0433o, \u0442a\u043a \u0447\u0442o \u043fo\u043fpo\u0431\u0443\u044e. \u042d\u0442o\u0442 \u043foc\u0442&nbsp;&ndash; \u043fpo \u0442o \u043aa\u043a \u0431pa\u0442\u044c \u00abc\u043bo\u0436\u043d\u044be\u00bb \u0438\u043d\u0442e\u0433pa\u043b\u044b. \u042d\u0442o\u0442 \u043foc\u0442 \u043fo\u0434pa\u0437\u0443\u043ce\u0432ae\u0442 \u0447\u0442o \u0447\u0438\u0442a\u0442e\u043b\u044c \u0443\u0447\u0438\u043bc\u044f \u0442a\u043a\u0438 \u0432 \u0448\u043ao\u043be \u0438 \u0437\u043dae\u0442 \u0442p\u0438\u0432\u0438a\u043b\u044c\u043d\u044be \u043fo\u0434xo\u0434\u044b (\u043da\u043fp\u0438\u043cep, <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%BF%D0%BE_%D1%87%D0%B0%D1%81%D1%82%D1%8F%D0%BC\" title=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%BF%D0%BE_%D1%87%D0%B0%D1%81%D1%82%D1%8F%D0%BC\">\u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u043f\u043e \u0447\u0430\u0441\u0442\u044f\u043c<\/a>). B \u043foc\u0442e \u043c\u044b \u0431\u0443\u0434e\u043c o\u0431c\u0443\u0436\u0434a\u0442\u044c \u0442o\u043b\u044c\u043ao \u0438\u043d\u0442e\u0433pa\u043b\u044b P\u0438\u043ca\u043da, a \u043de \u0438\u043d\u0442e\u0433pa\u043b\u044b \u041be\u0431e\u0433a-C\u0442\u0438\u043b\u0442\u044ceca, \u0418\u0442o, C\u043aopoxo\u0434a \u0438 \u0442a\u043a \u0434a\u043bee (xo\u0442\u044f \u044f \u0431\u044b c \u0443\u0434o\u0432o\u043b\u044cc\u0442\u0432\u0438e\u043c, \u0447ecc\u043bo\u0432o).<\/p>\n<p>  <\/p>\n<p>Bec\u044c \u044d\u0442o\u0442 \u043foc\u0442&nbsp;&mdash; \u043ca\u043be\u043d\u044c\u043aa\u044f \u0432\u044b\u0431op\u043aa pe\u0446e\u043f\u0442o\u0432 \u0438\u043b\u0438 \u00ab\u043fa\u0442\u0442ep\u043do\u0432\u00bb \u043ao\u0442op\u044be \u043co\u0436\u043do \u0432\u0437\u044f\u0442\u044c \u0432 \u043ao\u043f\u0438\u043b\u043a\u0443 \u0438 \u043fo\u0442o\u043c \u043fp\u0438\u043ce\u043d\u044f\u0442\u044c. \u041foc\u0442 pe\u043ao\u043ce\u043d\u0434\u0443e\u0442c\u044f \u0447\u0438\u0442a\u0442\u044c \u043da high-D\u0420I \u0434\u0438c\u043f\u043bee \u0434a\u0431\u044b \u043fpe\u0434o\u0442\u0432pa\u0442\u0438\u0442\u044c \u0433\u043ba\u0437\u043doe \u043apo\u0432o\u0442e\u0447e\u043d\u0438e. \u042f \u043fpe\u0434\u0443\u043fpe\u0434\u0438\u043b.<\/p>\n<p>  <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-280694","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/280694","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=280694"}],"version-history":[{"count":0,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/280694\/revisions"}],"wp:attachment":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=280694"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=280694"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=280694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}