1. **State the problem:** Calculate the limit $$\lim_{x \to 1} \left( \sqrt{2x - 1} - 1 \right)$$. 2. **Rewrite the expression:** The direct substitution $x=1$ gives $\sqrt{2(1) - 1} - 1 = \sqrt{1} - 1 = 0$, so the limit is of the form $0$. 3. **Use conjugate to simplify:** Multiply numerator and denominator by the conjugate to rationalize: $$\lim_{x \to 1} \frac{\sqrt{2x - 1} - 1}{1} \times \frac{\sqrt{2x - 1} + 1}{\sqrt{2x - 1} + 1} = \lim_{x \to 1} \frac{(\sqrt{2x - 1})^2 - 1^2}{\sqrt{2x - 1} + 1} = \lim_{x \to 1} \frac{2x - 1 - 1}{\sqrt{2x - 1} + 1}$$ 4. **Simplify numerator:** $$\lim_{x \to 1} \frac{2x - 2}{\sqrt{2x - 1} + 1} = \lim_{x \to 1} \frac{2(x - 1)}{\sqrt{2x - 1} + 1}$$ 5. **Evaluate the limit by direct substitution:** $$\frac{2(1 - 1)}{\sqrt{2(1) - 1} + 1} = \frac{0}{1 + 1} = 0$$ 6. **Final answer:** $$\boxed{0.00}$$