Examine whether the function f given by `f(x)=x^2`is continuous at `x = 0`.

Explanation

To determine whether the function \( f(x) = x^2 \) is continuous at \( x = 0 \), we need to check the following three conditions for continuity:

1. The function \( f(0) \) is defined.
2. The left-hand limit \( \lim_{x \to 0^-} f(x) \) exists.
3. The right-hand limit \( \lim_{x \to 0^+} f(x) \) exists.
4. The left-hand limit and right-hand limit are equal to the function value at that point, i.e., \( \lim_{x \to 0} f(x) = f(0) \).

Let's go through these steps one by one.
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