1. **State the problem:** We want to understand the expression $\frac{0}{0}$ and see if it can be represented as 0 using limits. 2. **Important note:** The expression $\frac{0}{0}$ is an indeterminate form, meaning it does not have a direct value. We use limits to analyze the behavior of functions that approach this form. 3. **Use limits:** Suppose we have two functions $f(x)$ and $g(x)$ such that $\lim_{x \to a} f(x) = 0$ and $\lim_{x \to a} g(x) = 0$. The limit of their quotient is $$\lim_{x \to a} \frac{f(x)}{g(x)}$$ which may or may not be 0. 4. **Example:** Let $f(x) = x^2$ and $g(x) = x$. Then $$\lim_{x \to 0} \frac{x^2}{x} = \lim_{x \to 0} x = 0$$ Here, the limit of the quotient is 0, even though directly substituting $x=0$ gives $\frac{0}{0}$. 5. **Conclusion:** $\frac{0}{0}$ is undefined, but using limits, the expression can approach 0 depending on the functions involved. Thus, $\lim_{x \to 0} \frac{x^2}{x} = 0$ is an example where the indeterminate form $\frac{0}{0}$ is represented by the limit 0.