Limite Fundamentale

  • May 2020
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Limite fundamentale (1+ f(x)) 1/f(x)= e

lim x-> x

dacă lim f(x)=+ x-> x

0

0

x-> x

n ∈ N, a>1

lim ln(1+f(x))/f(x)=1

lim f(x)=0

x-> x

x-> x

lim xn/ax=0



0

0 f(x)

lim (a -1)/f(x)=ln a

0

daca lim f(x)=0

x-> x

x-> x

0

0

r

lim [(1+x) -1)]/x=r x-> x

0

lim sin f(x) / f(x)=1

daca lim f(x)=0

x-> x

x-> x

0 f(x)

lim (e -1)/f(x)=1

0

daca lim f(x)=0

x->0

x-> x

0

Cazuri de excepţie 0/0

- lim de funcţii raţionale in puncte finite a - lim de funcţii in compunere cu funcţia modul - sub radical de ordine diferite figurează aceeaşi expresie - sub radical figurează expresii diferite - lim trigonometrice

Se face simplificarea prin (x-a)k Se explicitează modulul Se schimba variabila, notându-se radicalul de ordin egal cu cel mai mic multiplu comun al ordinelor radicalilor cu alta variabila Se amplifica numărătorul si (sau) numitorul cu expresia conjugata lim sin f(x) / f(x)= lim tg f(x) / f(x)= lim arcsin f(x) / f(x)= lim arctg f(x) / f(x)=1 x-> x 0

∞-∞ 1∞ 0

0

x-> x

x-> x

0

0

- lim de funcţii raţionale

Se aduce la acelaşi numitor

- lim de funcţii iraţionale

Se amplifica cu conjugata lim (1+ f(x)) 1/f(x)= e x-> x

0

lim x*ln x=0 si scrierea fg=e g* ln f x\>0

x-> x

0

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