Izisetshenziswa ezilethwayo izinombolo: izindlela ekubaleni nezibonelo

Mhlawumbe nomqondo esuselwe ejwayelene sonke kusukela esikoleni esiphakeme. Ngokuvamile abafundi kunzima ukuqonda lokhu ngokungangabazeki into ebaluleke kakhulu. It is ngenkuthalo esetshenziswa ezindaweni ezihlukahlukene ekuphileni kwabantu, futhi abaningi ubunjiniyela zazisekelwe ngokunembile izibalo sitholwe esuselwe. Kodwa ngaphambi kokuqhubeka ekuhlaziyweni yini esuselwe iinomboro lokha ukubala futhi lapho singaba usizo kabi, kokubuka kancane ku umlando.

indaba

Umqondo esuselwe, okuyinto ngesisekelo izingabunjalo, uvuliwe (ngcono nakakhulu ukuthi "yasungulwa" ngoba, ngenxa yalokho, alikho ngokwemvelo) Isaakom Nyutonom, ubani sonke siyazi kusukela ekutholakaleni umthetho wamandla adonsela phansi. Nguye owokuqala ezisetshenziselwa wathandeka kakhulu lo mqondo physics imvelo esibophezelayo ijubane nokusheshisa zemizimba. Futhi ososayensi abaningi siqhubeke nokumdumisa Newton salokhu okusungulile omangalisayo, ngoba eqinisweni wasungula ngesisekelo umehluko kanye calculus ebalulekile, ngesisekelo okuyiqiniso wonke umkhakha wezibalo okuthiwa "izingabunjalo". Kungakhathaliseki ngesikhathi uMklomelo KaNobel, Newton Cishe ngabe ngitholile okwami izikhathi ezimbalwa.

Hhayi ngaphandle nezinye izingqondo ezinkulu. Ngaphezu Newton on ukuthuthukisa wasebenza enjalo geniuses esuselwe futhi ebalulekile ovelele wezibalo njengoba Leonhard Euler, Lagrange futhi Louis Gotfrid Leybnits. Kuyinto ngiyabonga kubo esinalo imfundiso yokuziphendukela calculus umehluko ngesimo lapho ukhona kuze kube yilolu suku. Phela, lokhu Leibniz wathola incazelo weJiyomethri we esuselwe, okuyinto limane emthambekeni tangent kuya igrafu umsebenzi.

Uyini esuselwe izinombolo? Bit uphinda nalokho okwenzeka esikoleni.

Uyini esuselwe?

Chaza lo mqondo ngezindlela eziningana ezahlukene. Isizathu esilula: Derivatives - kuba izinga loshintsho umsebenzi. Okumela igrafu iyiphi y umsebenzi x. Uma ayiqondile, it has ezinye Curves kugrafu, kuthiwa izinkathi ukwanda nokuncipha. Uma uthatha noma iyiphi isikhawu kuncane isimiso, kuyoba ngqo umugqa ingxenye. Ngakho, i-ratio ubukhulu ingxenye encanyana ye y usayizi x bazihlela ngokubambisana, futhi uyoba esuselwe umsebenzi weyesi inikezwe. Uma sicabangela umsebenzi sisonke, kunokuba weyesi ethize, sithola umsebenzi we esuselwe, ie kwencika ezithile ku-X y.

Ngaphezu kwalokho, ngaphandle incazelo ezingokomzimba esuselwe njengoba umsebenzi ngesilinganiso ushintsho, kukhona umuzwa weJiyomethri. On ke, thina manje nixoxe.

Okwakushiwo weJiyomethri

Izisetshenziswa ezilethwayo izinombolo ngokwabo inombolo ethile ukuthi akuyona ukuliqonda ongaqhubeki injongo. It kuvela ukuthi esuselwe engabonisi nje kuphela ukukhula rate noma wehlise umsebenzi, kanye emthambekeni tangent kuya igrafu umsebenzi ngaleso sikhathi. definition Hhayi kucace ngokuphelele. Ake sihlole ke ngokuningiliziwe. Ake sithi ube igrafu umsebenzi (ukuthatha isithakazelo ijika). It has an isibalo esingapheliyo amaphuzu, kodwa kunezindawo lapho kuphela iphuzu elilodwa has a esiphezulu noma esiphansi. Ngokusebenzisa noma iyiphi iphuzu enjalo, ungakwazi ukudweba umugqa oqondile, okwakuyoholela perpendicular igrafu umsebenzi ngaleso sikhathi. Lo mugqa iyobizwa ngokuthi tangent. Ake sithi labetibambile ngifinyelele empambana ne OX axis. Ngakho etholwe phakathi tangent kanye OX ahlangene engela uzobe kunqunywa esuselwe. Ngaphezu kwakho konke, i-tangent le engela kuyoba kulinganiswe nakho.

Asikhulume okuncane mayelana amacala ikakhulukazi nemikhiqizo Ake sihlole izinombolo.

Ezimweni Special

Njengoba sekushiwo, nemikhiqizo izinombolo - value esuselwe at iphuzu elithile. Lapha, ngokwesibonelo, thatha umsebenzi y = x ^2. I esuselwe x - izinombolo, kodwa ngokuvamile - umsebenzi elilingana 2 * x. Uma sidinga ukubala esuselwe, isibonelo, endaweni x ₀ = 1, sithola y '(1) = 2 * 1 = 2. Kulula kabi. An icala ezithakazelisayo iyona esuselwe yenomboro eziyinkimbinkimbi. Ukuze ungene uthole incazelo eningiliziwe ngalokho inombolo eziyinkimbinkimbi, thina ngeke. Engingakusho nje ukuthi le nombolo equkethe okubizwa ngokuthi iyunithi ngengqondo - inombolo kabani square kulingana -1. Ukubala lokhu esuselwe kungenzeka kuphela ngaphansi kwezimo ezilandelayo:

1) Kumele kube khona ukuze nemikhiqizo lokuqala olungaphelele izingxenye kwangempela futhi ngamehlo engqondo y futhi X.

2) izimo Cauchy-Riemann elihlobene ne ukulingana ngokwengxenye ezichazwe esigabeni sokuqala.

Elinye icala ezithakazelisayo, nakuba ayengazi njengokuba nzima sangaphambilini, kuyinto esuselwe inombolo engenhle. Eqinisweni, noma iziphi izinombolo negative kungenziwa umelwe omuhle, iphindwe -1. Awu, esuselwe futhi umsebenzi njalo okulingana njalo siphindwe esuselwe umsebenzi.

Kuyoba ezithakazelisayo ukuze ufunde mayelana indima nemikhiqizo ekuphileni kwabo kwansuku zonke, futhi lokhu manje futhi baxoxe ngalo.

isicelo

Mhlawumbe ngamunye wethu okungenani kanye ekuphileni ukubamba ecabanga ukuthi wezibalo akunakwenzeka ukuba wusizo kuye ngokwami. Futhi into enjalo eziyinkimbinkimbi njengoba esuselwe cishe ayinakho ukusetshenziswa. Empeleni, izibalo - isayensi eyisisekelo, futhi zonke izithelo zawo eba ikakhulukazi i-physics, i-chemistry, ukufunda izinkanyezi ngisho umnotho. Esuselwe kwaphawula ukuqala izingabunjalo, owasinika lo ithuba bafika eziphethweni emagrafu imisebenzi, futhi siye safunda ukuba ahumushe imithetho yemvelo futhi ukubabuyisela kuzobazuzisa ngenxa yale mpatho.

isiphetho

Yiqiniso, akuwona wonke umuntu kungaba wusizo kuya esuselwe empilweni yangempela. Kodwa izibalo eba logic surely kudingeka. Hhayi lutho ngoba wezibalo ibizwa ngokuthi indlovukazi wesayensi: it aqukethe nolwazi oluyisisekelo lokuthi nezinye izindima yolwazi.