Question

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

Answer 1

$f(x)=\frac{x+1-1}{x+1}+\frac{x+1+1-1}{x+2}=\frac{x+1}{x+1}-\frac{1}{x+1}+\frac{x+2}{x+2}-\frac{1}{x+2}=1-\frac{1}{x+1}+1-\frac{1}{x+2}$
$lim_{x->Inf}{f(x)}=lim_{x->Inf}{<span>1-\frac{1}{x+1}+1-\frac{1}{x+2}</span>}=1-\frac{1}{Inf}+1-\frac{1}{Inf}=1-0+1-0=2$