1. **State the problem:** Evaluate the limit $$\lim_{x \to 0} \frac{\sqrt{x+1} - 2}{x - 3}$$. 2. **Recall the formula and rules:** When evaluating limits that result in indeterminate forms like $\frac{0}{0}$, we often use algebraic manipulation such as rationalizing the numerator. 3. **Check direct substitution:** Substitute $x=0$: $$\frac{\sqrt{0+1} - 2}{0 - 3} = \frac{1 - 2}{-3} = \frac{-1}{-3} = \frac{1}{3}$$ Since this is a defined value, the limit is $\frac{1}{3}$. 4. **Final answer:** $$\lim_{x \to 0} \frac{\sqrt{x+1} - 2}{x - 3} = \frac{1}{3}$$ Note: The provided answers 25 and 50 or -2\sqrt{3} do not correspond to this limit.