QuestionExample : Find 1) $\lim _{x \rightarrow \infty} \frac{\sqrt{x^{2}+1}}{x+1}$

Studdy Solution
Evaluate the limit as $x \to \infty$.
As $x \to \infty$, $\frac{1}{x^2} \to 0$ and $\frac{1}{x} \to 0$.
Thus, the expression simplifies to:
$\frac{\sqrt{1 + 0}}{1 + 0} = \frac{1}{1} = 1$
The value of the limit is:
$\boxed{1}$