1. The problem is to understand and find the limit of a function involving absolute values. 2. The general formula for limits is $$\lim_{x \to a} f(x) = L$$ where $L$ is the value that $f(x)$ approaches as $x$ approaches $a$. 3. Important rule: Absolute value $|x|$ is defined as $$|x| = \begin{cases} x, & x \geq 0 \\ -x, & x < 0 \end{cases}$$ which means the function behaves differently on either side of zero. 4. To find limits involving absolute values, consider the left-hand limit and right-hand limit separately. 5. For example, to find $$\lim_{x \to 0} |x|$$: - Left-hand limit: $$\lim_{x \to 0^-} |x| = \lim_{x \to 0^-} -x = 0$$ - Right-hand limit: $$\lim_{x \to 0^+} |x| = \lim_{x \to 0^+} x = 0$$ 6. Since both one-sided limits are equal, the limit exists and is $$0$$. This approach applies to any limit involving absolute values by splitting the function into cases based on the sign of the expression inside the absolute value.