Evaluating a Limit
Evaluate the limit:
$$\lim_{x \to \infty} \frac{\sqrt{x^2 + 1}}{x + 1}$$
As \( x \to \infty \), the limit becomes:
\[ \frac{\sqrt{x^2 + 1}}{x + 1} = \frac{x\sqrt{1 + \frac{1}{x^2}}}{x + 1} = \frac{\sqrt{1 + \frac{1}{x^2}}}{1 + \frac{1}{x}} \to \frac{1}{1} = 1 \]
Final Answer: \( \boxed{1} \)