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

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[latex]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}[/latex] [latex]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[/latex]

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