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The limit of the given function as \( x \) approaches 0 is:

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

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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.

Explore the concept of limits and L'Hôpital's Rule in calculus with a focus on indeterminate forms. Learn how to solve problems involving limits as x approaches 0, including the example \( \lim_{x \to 0} \frac{\sqrt{x+1} - 1}{x} = \frac{1}{2} \). Discover key techniques such as algebraic manipulation and L'Hôpital's Rule. Suitable for advanced high school students and calculus enthusiasts.

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