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

Răspuns :

[tex]f(x)= [tex]n= \lim_{x \to \infty} [/tex]
y=mx+n
[tex]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[/tex]
[tex]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[/tex]
y=x+3