fie f(x)=e^x
f `(x) =(e^x) `=e^x
I)x→-∞limf(x)=lim(e^x-x-1)=lime^x-lim(x)-1=e^(- ∞)--(-∞)-1=0+∞-1= +∞
II) x→+∞ limf(x)=lim(e^∞-x-1=∞-∞operatie fara sens.Reiei limita
limf(x)=limx*(e^x/x-1) (A
lime^x/x=∞/∞ Aplici teoremalui Lhospital
lime^x/x=lim(e^x) `/x `=lime^x=E^∞=∞
Te duci in (A si faci inlocuiriea
lime^x*(e^x/x-1)=e^∞(∞-1)=∞
