Răspuns
Explicație pas cu pas:
[tex] \lim_{x \to 0, x>0} f(x)=0 [/tex]
[tex]\lim_{x \to 0, x>0} [(1+f(x))^{\frac{1}{f(x)}}]^{\frac{f(x)}{\sqrt{x}}}=e^{ \lim_{x \to 0,x>0} \frac{f(x)} {\sqrt{x}} }=e^{1}=e[/tex]
[tex]\lim_{x \to 0,x>0} \frac{f(x)}{\sqrt{x}}=(0/0 l'Hospital)= \lim_{x \to \infty} 2\sqrt{x}f'(x) = \lim_{x \to 0, x>0} 2\sqrt{x}(\frac{2}{(x+1)ln5}+\frac{1}{2\sqrt{x}} )=0+1=1[/tex]
