# Find the limit, if it exists: lim_{x rightarrow infty}(8+frac{1}{x})

Find the limit, if it exists: $\underset{x\to \mathrm{\infty }}{lim}\left(8+\frac{1}{x}\right)$
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Tuthornt
Step 1 It is given that, $\underset{x\to \mathrm{\infty }}{lim}\left(8+\frac{1}{x}\right)$ Step 2 Obtain the value of $\underset{x\to \mathrm{\infty }}{lim}\left(8+\frac{1}{x}\right)$ as, $\underset{x\to \mathrm{\infty }}{lim}\left(8+\frac{1}{x}\right)=\underset{x\to \mathrm{\infty }}{lim}8+\underset{x\to \mathrm{\infty }}{lim}\frac{1}{x}$
$=8+0$
$=8$ Step 3 Therefore, the value of $\underset{x\to \mathrm{\infty }}{lim}\left(8+\frac{1}{x}\right)\text{is}8.$