The problem involves evaluating the limit:

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

Substituting $x = 1$ directly into the expression, we get:

$\frac{\sqrt{1} - \sqrt{2(1) - 1}}{1 - 2} = \frac{1 - \sqrt{1}}{-1} = \frac{1 - 1}{-1} = \frac{0}{-1} = 0$

So, the limit evaluates to:

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

Would you like further details on how this solution was reached, or do you have any specific questions?

Here are five related questions you might find interesting:

1. How do you evaluate limits when the direct substitution leads to an indeterminate form?
2. What are the different techniques to solve limits involving square roots?
3. Can L'Hôpital's rule be applied to solve this limit, and if so, how?
4. How would the limit change if the expression under the square roots were different?
5. How do you deal with limits that involve absolute value functions?

Tip: When evaluating limits, always check for indeterminate forms like $\frac{0}{0}$ or $\frac{\infty}{\infty}$ to decide if further techniques are needed.