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Forum Studenti •Piccola precisione sui limiti
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Piccola precisione sui limiti

Inviato: sabato 13 febbraio 2016, 10:49
da Giuseppe95
Una funzione limitata e definita su un intervallo limitato, ammette limite negli estremi dell'intervallo? Perchè pur essendo essi dei punti di accumulazione, si può calcolare solo il limite destro dell'estremo sinistro ma non il limite sinistro dato che a sinistra del punto non c'è niente (analogamente per l'estremo destro).
Per esempio nell'immagine che ho allegato, il limite di f(x) per x che tende a 4 esiste? Perchè in questo caso esiste il limite sinistro ma non il destro
Immagine.png
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Re: Piccola precisione sui limiti

Inviato: sabato 13 febbraio 2016, 23:04
da Carmine
Per convenzione, in questi casi si dice che f ammette limite in a, derivata prima in a, derivata k-esima in a, se esistono i rispettivi limiti destri (analogamente coi limiti sinistri per b). Occhio però, non è sempre detto che una funzione limitata in un intervallo chiuso ammetta limite destro in a (Un esempio?).