Evaluate the following limits :
`Lim_(x to 0 ) (x^(n)-1)/(x-1)`

Answer

To evaluate the limit

\[ \lim_{x \to 0} \frac{x^n - 1}{x - 1}, \]

we will follow these steps:

### Step 1: Substitute \( x = 0 \)

First, we substitute \( x = 0 \) into the expression to check if it results in an indeterminate form.

\[ \frac{0^n - 1}{0 - 1} = \frac{-1}{-1} = 1. \]

### Step 2: Conclusion

Since substituting \( x = 0 \) gives us a determinate form (1), we can conclude that:

\[ \lim_{x \to 0} \frac{x^n - 1}{x - 1} = 1. \]

### Final Answer

Thus, the limit evaluates to:

\[ \boxed{1}. \]

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