Question

AM 136 admitere UPT 2020

Answer 1

Răspuns:

Explicație pas cu pas:

pentru x=1, f(1)=1·√0=0

pentru x>1, evident f(x)>0

Calculam limita la +∞

$\lim_{ \to +\infty} [x*\sqrt{\frac{x-1}{x+1}}]= \lim_{ \to +\infty} [x*\sqrt{\frac{x+1-1-1}{x+1}}]= \lim_{ \to +\infty} [x*\sqrt{1-\frac{2}{x+1}}]=\lim_{ \to +\infty} x*\lim_{ \to +\infty}\sqrt{1-\frac{2}{x+1}}=+\infty*1=+\infty$

Deci Im f(x)=[0,+∞).