1. **State the problem:** We need to find the limit $$\lim_{x \to 0} \frac{x^3}{x}$$. 2. **Simplify the expression:** Since $x \neq 0$ in the limit process (we approach 0 but never equal to 0), we can simplify: $$\frac{x^3}{x} = x^{3-1} = x^2$$ 3. **Rewrite the limit:** Now the limit becomes: $$\lim_{x \to 0} x^2$$ 4. **Evaluate the limit:** As $x$ approaches 0, $x^2$ approaches 0 because squaring a number close to zero makes it even closer to zero. 5. **Conclusion:** Therefore, $$\lim_{x \to 0} \frac{x^3}{x} = 0$$ This limit exists and equals 0. 6. **Graph explanation:** The function simplifies to $y = x^2$, which is a parabola opening upwards with vertex at the origin. The graph is continuous and smooth at $x=0$, confirming the limit value.