https://file.aiquickdraw.com/mathbot/file/1727072660846qd1783id.jpg

The mathematical expression in the image is:

\[
\lim_{{x \to 4}} \frac{4x^3 - 48}{x^2 - 12}
\]

### Step-by-step solution:

1. **Substitute** \( x = 4 \) into the function directly:

   \[
   \frac{4(4)^3 - 48}{(4)^2 - 12} = \frac{4(64) - 48}{16 - 12} = \frac{256 - 48}{4} = \frac{208}{4} = 52
   \]

Therefore, the limit is:

\[
\lim_{{x \to 4}} \frac{4x^3 - 48}{x^2 - 12} = 52
\]

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Would you like further details or have any questions on the solution?

Here are 5 related questions you might find interesting:

1. What happens if the denominator approaches zero in a limit?
2. How do you factor and simplify limits involving polynomials?
3. What is the difference between limits approaching finite values and limits approaching infinity?
4. How can L'Hopital's rule be applied to solve limits involving indeterminate forms?
5. What are common techniques to evaluate limits when direct substitution doesn’t work?

**Tip:** Always check if direct substitution in a limit works before using more advanced techniques!

Find the limit as x approaches 4 of the function (4x^3 - 48) / (x^2 - 12).

Explore the step-by-step process of solving the limit of the function (4x^3 - 48) / (x^2 - 12) as x approaches 4. This problem delves into key concepts of limits and polynomial functions, utilizing direct substitution to find the limit.

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