Question

how to compute the limit as x approaches positive infinite of: sqrt(x)/(1+x)

Answer 1

\[\frac{\sqrt x}{1+x}=\frac1{\frac1{\sqrt x}+\sqrt x}\]\[\lim_{x \rightarrow \infty }\frac1{\frac 1{\sqrt x}+\sqrt{x}}=0\]

Answer 2

\[\lim_{x \rightarrow \infty }\frac1{\sqrt x}=0\]
so the previous one becomes
\[\lim_{x \rightarrow \infty }\frac{1}{0+\sqrt x}=\lim_{x \rightarrow \infty }\frac{1}{\sqrt x}=0^{+}\]