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To compute the limit \(\lim_{x \to 1} (2x - 2)^3\), we can directly substitute \(x = 1\) into the expression since the function is continuous at \(x = 1\).

Let's go through the steps:

1. First, simplify the expression inside the cube:
   \[
   2x - 2 = 2(1) - 2 = 0
   \]

2. Now, take the cube of the result:
   \[
   (2x - 2)^3 = 0^3 = 0
   \]

Therefore, the limit is:

\[
\lim_{x \to 1} (2x - 2)^3 = 0
\]

Would you like more details on limits or have any questions?

Here are 5 related questions:
1. How do you compute limits for functions that are not continuous?
2. What happens when the limit leads to an indeterminate form like \(\frac{0}{0}\)?
3. Can you explain the difference between one-sided and two-sided limits?
4. How do we evaluate limits involving infinity?
5. When should we use L'Hopital's Rule for limits?

**Tip**: For polynomial and rational functions, direct substitution often works to compute limits if the function is continuous at the point of interest.

Compute the following limit: lim (x → 1) (2x - 2)^3

Learn how to calculate the limit of (2x - 2)^3 as x approaches 1 using direct substitution. This problem illustrates key concepts in limits and polynomial continuity, making it ideal for high school students (Grades 10-12).

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