The limit of the given function as $x$ approaches 0 is:

$\lim_{{x \to 0}} \frac{\sqrt{x+1} - 1}{x} = \frac{1}{2}$

Would you like further details or have any questions?

Here are 5 questions you might want to ask next:

1. How do you solve limits involving indeterminate forms?
2. Can you explain the concept of L'Hôpital's Rule?
3. How do you find the derivative of a function?
4. What are some common techniques for evaluating limits?
5. How do you handle limits at infinity?

Tip: When evaluating limits that result in indeterminate forms like $\frac{0}{0}$, consider using algebraic manipulation or L'Hôpital's Rule to find the limit.