Question

f:(3,+infinit)=>R, f(x)=xpatrat/x-3. Scrieti ecuatia asimptotei oblice catre +infinit la graficul functiei f

Answer 1

$f(x)= [tex]n= \lim_{x \to \infty}$
y=mx+n
$m =\lim_{x \to \infty} \frac{f(x)}{x} = \lim_{x \to \infty} \frac{ x^{2} }{x(x-3)} = \lim_{x \to \infty} \frac{ x^{2} }{ x^{2} -3x} =1$
$n= \lim_{x \to \infty} [f(x)-mx]= \lim_{x \to \infty} (\frac{ x^{2} }{x-3}-x)= \\ \lim_{x \to \infty} \frac{3x}{x-3} =3$
y=x+3