{"id":531,"date":"2026-10-30T15:17:08","date_gmt":"2026-10-30T13:17:08","guid":{"rendered":"https:\/\/liceubolintin.ro\/eduhub\/?p=531"},"modified":"2026-10-30T15:17:08","modified_gmt":"2026-10-30T13:17:08","slug":"asimptote-prof-ioana-costache","status":"publish","type":"post","link":"https:\/\/liceubolintin.ro\/eduhub\/2026\/10\/30\/asimptote-prof-ioana-costache\/","title":{"rendered":"Asimptote – Prof. Ioana Costache"},"content":{"rendered":"
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Asimptopte folosind Metoda PROIECTULUI<\/h1>\n<\/header>\n
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Proiect de lec\u021bie<\/h2>\n

Profesor: <\/em>Costache Ioana Corina<\/em><\/strong><\/p>\n

Clasa: <\/em>a 11 \u00a0a\u00a0 A<\/p>\n

Disciplina: <\/em>MATEMATIC\u0102<\/p>\n

Unitate de invatare: recapitulare \u0219i sistematizare<\/em><\/p>\n

Tema: <\/em>Asimptotele unei func\u021bii<\/strong><\/p>\n

Tipul lectiei: <\/em>consolidare \u0219i sistematizare<\/p>\n

COMPETENTE SPECIFICE<\/p>\n

1. Caracterizarea<\/strong> unor func\u0163ii utiliz\u00e2ndreprez geom a unor cazuri particulare;<\/p>\n

2. Interpretarea<\/strong> unor propriet\u0103\u0163i ale func\u0163iilor cu ajut reprezent grafice;<\/p>\n

3. Aplicarea<\/strong> unor algoritmi specificicalculului diferen\u0163ial \u00een rez unorprobl;<\/p>\n

4. Exprimarea<\/strong> cu aj no\u0163 de limit\u0103,a unor propr cantit \u015fi calit ale unei func\u0163ii;<\/p>\n

5. Utilizarea<\/strong> reprezent\u0103rii grafice a uneifunc\u0163ii pentru verificarea unor rezultate \u015fipentru identificarea unor propriet\u0103\u0163i;<\/p>\n

OBIECTIVE\u00a0 OPERA\u0162IONALE: la finalul orei elevii vor fi capabili s\u0103:<\/p>\n

\u00a0<\/strong>s\u0103 defineasca asimptota verticala \/ oblica\/ orizontala<\/p>\n

\u00a0:<\/strong> s\u0103 cunoasc\u0103 formulele pentru calculul elementelor m si n ale asimptotelor oblice<\/p>\n

\u00a0:<\/strong> s\u0103 aplice \u00een practic\u0103 formulele pentru calculul elementelor m si n ale asimptotelor oblice<\/p>\n

O : s\u0103 recunoasca diferitele tipuri de asimptote ale unei functii<\/p>\n

\u00a0\u00a0\u00a0\u00a0 O : \u00a0sa determine diverse tipuri de asimptote<\/p>\n

STRATEGII DIDACTICE:<\/em><\/p>\n

Metode \u015fi procedee\u00a0: <\/strong>conversa\u0163ia, explica\u0163ia, observa\u0163ia, expunerea, exerci\u0163iul.,proiectul.<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Mijloace \u015fi materiale didactice: <\/strong>manual, culegeri, fi\u015f\u0103 de lucru, tabla, creta<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Forme de organizare: <\/strong>individuala, pe echipe<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Moduri de activitate cu elevi<\/strong>: Consolidarea teoriei prin practic\u0103<\/p>\n

Surse bibliografice<\/strong>:<\/p>\n

\u00a0Marius si Georgeta Burtea \u2013 Matematic\u0103 manual pentru clasa a XI-a trunchi comun \u0219i diferen\u021biat , Ed.Carminis2005.<\/p>\n

Marius Burtea, <\/strong>Culegere Matematioca M2 clasa a XI-a, Editura Campion, Bucuresti, 2009<\/p>\n

SubiectesimulareBAC<\/p>\n

DESF\u0102\u015eURAREA\u00a0 LEC\u0162IEI<\/em><\/strong><\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n\n
Etapele lec\u0163iei<\/strong><\/td>\nObiectivele vizate<\/strong><\/td>\n\u00a0<\/strong> Con\u0163inutul lec\u0163iei<\/strong><\/td>\nStrategiile didactice<\/strong><\/td>\n<\/td>\n<\/tr>\n
Metode \u015fi procedee<\/strong><\/td>\nForme de activitate<\/strong><\/td>\n<\/td>\n<\/tr>\n
Activitatea profesorului<\/strong><\/td>\nActivitatea elevului<\/strong><\/td>\n<\/td>\n<\/tr>\n
1<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n6<\/td>\n<\/td>\n<\/tr>\n
Moment organizatoric<\/strong> 1\u2019<\/strong><\/td>\n<\/td>\n-noteaz\u0103 absentele Elevii preg\u0103tesc manualele, caietele de noti\u0163e, caietele de teme, instrumentele de scris.<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Captarea atentiei:<\/strong> Anuntarea titlului lectiei<\/strong> 1\u2019<\/strong><\/td>\n<\/td>\n-noteaz\u0103 titlul lectie pe tabla -anun\u0163\u0103 obiectivele pe care si-a propus sa le ating\u0103<\/td>\n-elevii notez\u0103 titlul lec\u0163ie in caiete<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Actualizarea cuno\u015ftin\u0163elor<\/strong> 15\u2019<\/strong><\/td>\nO1 \u00a0 O2<\/td>\nRecapitularea tipurilor de asimptote: Defini\u021bii, tipuri de asimptote, metode de determinare \u00a0a fiec\u0103rui tip studiteIdentificarea \/recunoa\u0219terea asimptotelor pe graficul unei func\u021bii Ce intelegem prin asimtota a unei functii? \u00a0 Ce este o asimptota veriticala? \u00a0 Observatie. <\/em>Dreapta x=a este o dreapta paralela cu Oy, deci verticala. Ce functii admit asiptote verticale? \u00a0<\/em> Observatii.<\/em> Pentru existenta asimptotei verticale nu este necesar ca functia sa fie definita in a.Admit asimptote verticale:functiile ale caror legi de corespondenta sunt exprimate prin fractii, \u00een punctele \u00een care se anuleaza numitorulfunctiile ale caror legi de corespondenta sunt exprimate prin logaritmi, , \u00een punctele pentru care g(x)=0 \u00a0 Se rezolva exercitiul2(b) de pe fisa de lucru. \u00a0 Definitie. <\/strong>Fie functia , astfel incat \u00a0este punct de acumulare al lui I. Spunem ca dreapta y=b este asimptota orizontala a lui f spre \u00a0daca , respectiv . Observatii<\/em>. Dreapta y=b este paralela cu axa Ox. Nu are sens sa cautam asimptote orizontale spre \u00a0daca functia nu este definita spre\u00a0\u00a0 . Se rezolva exercitiul 2 (b)de pe fisa de lucru. \u00a0<\/strong> Observatii<\/em>. 1) <\/em>Pentru determinarea asimptotei oblice se procedeaza astfel: se calculeaza ;daca m este finit, atunci se calculeaza\u00a0 ;daca si n este finit atunci dreapta\u00a0 \u00a0reprezinta asimptota oblica alui f spre \u00a0 Observatie<\/em> :O functie nu poate admite atat asimptota orizontala cat si oblica spre ( ). Se rezolva exercitiul 3 de pe fi\u0219\u0103.<\/td>\nasimptota este \u00a0o dreapta fata de care graficul unei functii \u201ese apropie oricat de mult \u00a0 \u00a0 \u00a0 Fie \u00a0punct de acumulare. Definitie.\u00a0 <\/strong>\u00a0dreapta x = x0<\/sub> este asimptot\u0103 vertical\u0103 la graficul func\u0163iei f(x), dac\u0103 cel pu\u0163in una din limitele laterale ale func\u0163iei f \u00een punctul x0 <\/sub>este infinit\u0103.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 . \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Elevii identific\u0103 asimptotele pe grafic\/ fisa de lucru\u00a0 \u00a0<\/em><\/td>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 conversatia<\/td>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 frontala<\/td>\n<\/td>\n<\/tr>\n
Consolidarea \u0219i sistematizarea \u00a0cunostintelor<\/strong> 35\u2019<\/strong><\/td>\n\u00a0 O1 O2 O3 O4<\/td>\nElevii primesc Fisa de lucru \u00a0 Elevii din fiecare grupa rezolva exercitiile de pe fisa primita. Apoi seful echipei iese la tabla pentru a prezenta rezolvarea.<\/td>\nRezolva exercitiile, compar\u00e2nd propriile rezultate cu cele de pe tabl\u0103. \u00a0 -Elevii vor nota in caiete\u00a0 rezolvarile propuse si se va rezolva si la tabla cateva din aplicati<\/td>\n\u00a0 \u00a0 Conversatia \u00a0 \u00a0 Exercitiul<\/td>\n\u00a0 \u00a0 \u00a0 Frontala<\/td>\n<\/td>\n<\/tr>\n
Feed-back<\/strong> 2<\/strong>\u2019<\/strong><\/td>\n<\/td>\nCare sunt etapele in a determina asimptotele unei functii? Cand o graficul unei func\u021bii admite asimptote verticale? Dar orizontale\/ oblice?<\/td>\nElevii sunt aten\u0163i \u015fi r\u0103spund la \u00eentreb\u0103rile profesorului<\/td>\nExercitiul<\/td>\nIndividual<\/td>\n<\/td>\n<\/tr>\n
Evaluarea<\/strong> 1\u2019<\/strong><\/td>\n<\/td>\nAprecierea raspunsurilor primite Tema acasa- restul exerci\u021biilor de pe fis\u0103<\/td>\nNoteaz\u0103 tema<\/td>\nfrontal\u0103<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n

Anexa 1.<\/p>\n

JOCUL LIMITELOR<\/p>\n

NIVELUL 1<\/p>\n

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  1. PREA CALD!<\/li>\n<\/ol>\n

    Temperatura unui computer nu poate dep\u0103\u0219i 70 \u00b0C. Pentru ca acesta s\u0103 nu se deterioreze datorit\u0103 supra\u00eenc\u0103lzirii, cel mai adesea porne\u0219te un ventilator care face ca asemenea probleme s\u0103 nu se \u00eent\u00e2mple, r\u0103cind componentele calculatorului. Atunci c\u00e2nd porne\u0219te ventilatorul temperatura se schimb\u0103 conform urm\u0103toarei legi: \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 T = 40 .<\/sup> (1\/2)t<\/sup> + 30<\/p>\n

    T = temperatura \u00een grade Celsius, t = timpul \u00een minute<\/p>\n

    C\u0103tre ce valoare tinde temperatura intern\u0103?<\/p>\n

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    • CRE\u0218TEREA POPULA\u021aIEI<\/li>\n<\/ul>\n

      Urm\u0103toarea func\u021bie:<\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 300t2<\/sup> + 120t +420<\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 f(t) = ______________________<\/sup><\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10t2<\/sup> + 5t + 20<\/p>\n

      stabile\u0219te num\u0103rul (\u00een mii de locuitori) ai unui ora\u0219 dup\u0103 t ani din acest moment.<\/p>\n

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      1. C\u00e2\u021bi locuitori locuiesc \u00een ora\u0219 \u00een acest moment?<\/li>\n
      2. C\u00e2\u021bi locuitori vor locui \u00een ora\u0219 peste un an?<\/li>\n
      3. C\u00e2\u021bi locuitori vor fi dup\u0103 un timp \u00eendelungat? (adic\u0103 poate nr. acestora s\u0103 creasc\u0103 f\u0103r\u0103 limite?)<\/li>\n<\/ol>\n