Elemente de Analiza matematica a XI-a

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Aceasta sectiune cuprinde elemente de analiza matematica studiate in clasa a XI-a , si anume : siruri , limite de siruri , limite de functii , functii continue , functii derivabile , proprietatile functiilor derivabile , grafice de functii si probleme recapitulative . Sectiunea cuprinde si seturi de probleme propuse si rezolvate aferente fiecarui capitol studiat .

Siruri . Limite de siruriIn acest capitol definim si prezentam notiunile de : sir , siruri marginite , siruri monotone , vecinatati pe axa reala , siruri convergente , limita unui sir , siruri divergente , operatii cu siruri convergente , teoreme de convergenta , criterii de convergenta a sirurilor , dreapta reala incheiata , siruri tip , siruri remarcabile , calculul limitelor sirurilor remarcabile , calculul limitelor de siruri in cazurile de nedeterminare , alte probleme cu limite de siruri , Lema lui Stolz-Cesaro , criteriul radacinii , criteriul clestelui , Teorema lui Cantor , Teorema lui Weierstrass , definitia numarului irational e , siruri recurente si altele .

Limite de functiiIn acest capitol definim si studiem limite de functii .Capitolul contine limite de functii rezolvate .

Functii continueIn acest capitol definim si studiem functii continue . Capitolul cuprinde : 1.) Continuitatea punctuala : continuitatea unei functii intr-un punct ; continuitatea unei functii pe un interval ; continuitate laterala ; puncte de discontinuitate ; prelungirea prin continuitate a unei functii intr-un punct ; concluzii finale privind continuitatea punctuala . 2.) Operatii cu functii continue . 3.) Proprietati ale functiilor continue ; proprietatea lui Darboux . 4.) Proprietatile functiilor continue pe un interval inchis .

Functii derivabileIn acest capitol definim si studiem functii derivabile . Capitolul functii derivabile cuprinde :

Tabel cu derivatele functiilor elementareIn acest subcapitol prezentam tabelul cu derivate ale functiilor elementare .

Tabel cu derivate ale functiilor compuseIn acest subcapitol prezentam tabelul cu derivate ale functiilor compuse . Exemple de derivate compuse .