Chii chinonzi Bolzano Theorem chinosimbisa?
Muenzaniso weiyo Bolzano Theorem
Tora semuenzaniso basa f(x) = x³ + x − 1. Isu tinoziva kuti ibasa rinoenderera nekuti iri polynomial. Kana tikaongorora basa pamagumo enguva , iva:
- f(0) = -1 (negative)
- f(1) = 1 (zvakanaka)
Sezvo theorem inoda kuti zviratidzo zvipesana, tinogona kushandisa Bolzano kugumisa kuti kune kukosha c mukati menguva (0,1) kupi f(c) = 0. Mhedzisiro iyi haitiudzi kuti kukosha uku chii, asi kunovimbisa kuvepo kwayo. Pamusoro pezvo, zvekufungidzira matekiniki, unogona kushandisa nzira senge bisection dzinotsanangurwawo muchikamu chedu chakatsaurirwa Bolzano's theorem: mienzaniso uye mashandisirwo munhamba nzira.
Zvishandiso zveBolzano's Theorem
- Tsvaga midzi: Inonyanya kukosha mu , iyo inoparadzanisa nguva dzenguva kuti ifananidze mudzi zvakanyatsorongeka. Aya maitiro ane chekuitawo nebasa re.
- Ongororo yeanoramba achiita: Inobatsira kunzwisisa maitiro emabasa panguva dzakatarwa, kuona zvakakosha mapoinzi semidzi kana mapoinzi akakosha.
- Injiniya kugadzirisa dambudziko: Kubva pakugadzira dhizaini kusvika pakumanikidza kuongororwa, theorem inoshandiswa kuona mapoinzi panowanikwa mamwe mamiriro akakomba.
- Algorithms mukombuta: Inoshandiswa muzvirongwa zvekuongorora nhamba kugadzirisa nonlinear equations isina mhinduro yakananga yekuongorora.
Nhoroondo yeBolzano Theorem
Uchapupu hweBolzano's Theorem
- Govanisa nguva yekutanga kuita zvikamu zviviri zvakaenzana uye ongorora basa riri pakati.
- Sarudza mune ipi yezvikamu zvishoma kukosha kwebasa rinoshandura chiratidzo.
- Dzokorora iyo nzira muchikamu chenguva yakasarudzwa kusvika chaiyo yaunoda yasvika, tichiwedzera kuve nechokwadi chekuti tinoswedera pedyo nemudzi.
