👤
a fost răspuns

f:[0,+infinit) ->R f(x)=x/x+1 + x+1/x+2. Calculati limita cand x tinde la +infinit din f(x)

Răspuns :

[tex]f(x)=\frac{x+1-1}{x+1}+\frac{x+1+1-1}{x+2}=\frac{x+1}{x+1}-\frac{1}{x+1}+\frac{x+2}{x+2}-\frac{1}{x+2}=1-\frac{1}{x+1}+1-\frac{1}{x+2}[/tex]
[tex]lim_{x->Inf}{f(x)}=lim_{x->Inf}{1-\frac{1}{x+1}+1-\frac{1}{x+2}}=1-\frac{1}{Inf}+1-\frac{1}{Inf}=1-0+1-0=2[/tex]

Alte intrebari