1. **State the problem:** Find the limit $$\lim_{x \to 1} 4^{\frac{2x - 2}{x}}$$. 2. **Recall the limit and exponential rules:** The limit of an exponential function $$a^{f(x)}$$ as $$x$$ approaches a value can be found by evaluating the exponent's limit first, provided the base $$a > 0$$ and $$a \neq 1$$. 3. **Evaluate the exponent's limit:** $$\lim_{x \to 1} \frac{2x - 2}{x} = \lim_{x \to 1} \frac{2(x - 1)}{x}$$. 4. **Substitute $$x = 1$$ directly:** $$\frac{2(1 - 1)}{1} = \frac{0}{1} = 0$$. 5. **Apply the limit to the original expression:** $$4^0 = 1$$. **Final answer:** $$\lim_{x \to 1} 4^{\frac{2x - 2}{x}} = 1$$.