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The problem asks to evaluate the limit of the function \( f(x) = 5x^2 - 9x - 4 \) as \( x \) approaches 3.

### Steps:
1. The function given is a polynomial, and limits of polynomials can be evaluated by direct substitution.
   
   \[
   \lim_{x \to 3} f(x) = f(3)
   \]

2. Substitute \( x = 3 \) into the function:

   \[
   f(3) = 5(3)^2 - 9(3) - 4
   \]

3. Calculate the terms:

   \[
   f(3) = 5(9) - 27 - 4 = 45 - 27 - 4 = 14
   \]

Thus, the limit is:

\[
\lim_{x \to 3} f(x) = 14
\]

Would you like further details or explanations?

Here are some related questions you can explore:
1. How do you evaluate limits of more complex functions?
2. What happens if the limit approaches infinity instead of a specific number?
3. What is the difference between left-hand and right-hand limits?
4. How would you compute limits for non-polynomial functions?
5. Can a function have a limit if it has a discontinuity at that point?

**Tip:** When evaluating limits of polynomial functions, you can always substitute the point directly because polynomials are continuous everywhere.

Suppose f(x) = 5x^2 - 9x - 4. Evaluate: lim(x→3) f(x)

This problem demonstrates how to evaluate the limit of the polynomial function f(x) = 5x^2 - 9x - 4 as x approaches 3 using direct substitution. Learn about polynomial limits and continuous functions.

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