Show that `f(x)=|x|` is continuous at x=0

Explanation

To show that the function \( f(x) = |x| \) is continuous at \( x = 0 \), we need to verify the definition of continuity at that point. A function \( f(x) \) is continuous at \( x = a \) if the following three conditions are satisfied:

1. \( f(a) \) is defined.
2. \( \lim_{x \to a} f(x) \) exists.
3. \( \lim_{x \to a} f(x) = f(a) \).

In this case, we will check these conditions for \( a = 0 \).

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