To evaluate the limit of the function \( f(x) = x^3 + 2x^2 - 3x - 4 \) as \( x \) approaches \(-1\), we simply substitute \( x = -1 \) into the expression:

\[
f(x) = x^3 + 2x^2 - 3x - 4
\]

Substituting \( x = -1 \):

\[
f(-1) = (-1)^3 + 2(-1)^2 - 3(-1) - 4
\]

Now, let's calculate each term:

\[
(-1)^3 = -1, \quad 2(-1)^2 = 2 \times 1 = 2, \quad -3(-1) = 3, \quad -4 = -4
\]

Adding these together:

\[
f(-1) = -1 + 2 + 3 - 4 = 0
\]

Therefore, the limit is:

\[
\lim_{x \to -1} (x^3 + 2x^2 - 3x - 4) = 0
\]

Would you like further clarification or details on how this works?

Here are five related questions to explore further:
1. How do you find limits using L'Hôpital's Rule?
2. What happens when a limit leads to an indeterminate form like \( \frac{0}{0} \)?
3. Can all polynomials be solved using direct substitution for limits?
4. How do limits behave at infinity for polynomial functions?
5. What is the significance of one-sided limits?

**Tip**: When calculating limits of polynomials, direct substitution is usually the most efficient method unless the expression results in an indeterminate form.

This solution explains how to find the limit of the polynomial function x^3 + 2x^2 - 3x - 4 as x approaches -1. It uses direct substitution to solve the problem, making it suitable for high school calculus students. Explore key concepts in limits and polynomial behavior.

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