Prove that the function `f(x)=x^n`is continuous at `x = n`, where n is a positive integer.

Explanation

To prove that the function \( f(x) = x^n \) is continuous at \( x = n \), where \( n \) is a positive integer, we will follow the definition of continuity. A function \( f \) is continuous at a point \( c \) if:

\[ \lim_{x \to c} f(x) = f(c) \]

### Step 1: Identify the point of continuity
We need to check the continuity of \( f(x) \) at \( x = n \).
...