Question

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Answer 1

Răspuns

Explicație pas cu pas:

$\lim_{x \to 0, x>0} f(x)=0$

$\lim_{x \to 0, x>0} [(1+f(x))^{\frac{1}{f(x)}}]^{\frac{f(x)}{\sqrt{x}}}=e^{ \lim_{x \to 0,x>0} \frac{f(x)} {\sqrt{x}} }=e^{1}=e$

$\lim_{x \to 0,x>0} \frac{f(x)}{\sqrt{x}}=(0/0 l'Hospital)= \lim_{x \to \infty} 2\sqrt{x}f'(x) = \lim_{x \to 0, x>0} 2\sqrt{x}(\frac{2}{(x+1)ln5}+\frac{1}{2\sqrt{x}} )=0+1=1$