1. **Stating the problem:** We want to understand what an indeterminate form is in calculus and see a numerical example. 2. **Definition:** An indeterminate form occurs when evaluating a limit results in an expression like $\frac{0}{0}$ or $\frac{\infty}{\infty}$, which does not directly tell us the limit's value. 3. **Common indeterminate forms:** $0/0$, $\infty/\infty$, $0 \times \infty$, $\infty - \infty$, $0^0$, $1^\infty$, and $\infty^0$. 4. **Example:** Consider the function $f(x) = \frac{x^2 - 4}{x - 2}$ and find $\lim_{x \to 2} f(x)$. 5. **Direct substitution:** Substitute $x=2$: $$\frac{2^2 - 4}{2 - 2} = \frac{4 - 4}{0} = \frac{0}{0}$$ which is an indeterminate form. 6. **Resolving the indeterminate form:** Factor numerator: $$x^2 - 4 = (x - 2)(x + 2)$$ 7. **Simplify the function:** $$f(x) = \frac{(x - 2)(x + 2)}{x - 2}$$ For $x \neq 2$, this simplifies to: $$f(x) = x + 2$$ 8. **Evaluate the limit:** Now, $$\lim_{x \to 2} f(x) = \lim_{x \to 2} (x + 2) = 2 + 2 = 4$$ 9. **Conclusion:** Although direct substitution gave an indeterminate form $\frac{0}{0}$, simplifying the function allowed us to find the limit is 4. This illustrates how indeterminate forms require algebraic manipulation or other techniques to evaluate limits.