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The problem asks to calculate the limit of the function:

\[
\lim_{{x \to 2}} f(x) = x^3 - 5x^2 + 3x - 4
\]

To solve this, we can substitute \( x = 2 \) directly into the function, as the function is continuous at this point.

Let's evaluate:

\[
f(2) = (2)^3 - 5(2)^2 + 3(2) - 4
\]
\[
= 8 - 5(4) + 6 - 4
\]
\[
= 8 - 20 + 6 - 4
\]
\[
= -10
\]

Thus, the limit is:

\[
\lim_{{x \to 2}} f(x) = -10
\]

So, the correct answer is **-10**.

Do you need further details or explanations? Here are some related questions for practice:

1. What is the definition of a limit in calculus?
2. How do you determine if a function is continuous at a certain point?
3. What are the conditions for applying direct substitution when calculating limits?
4. How do limits behave with polynomial functions in general?
5. Can limits exist even if the function is undefined at the point?

**Tip:** For polynomial functions, you can usually evaluate limits directly by substituting the value of \( x \) if the function is continuous at that point.

Calcule el límite de la siguiente función: lim x→2 f(x) = x^3 - 5x^2 + 3x - 4

Learn how to calculate the limit of the function f(x) = x^3 - 5x^2 + 3x - 4 as x approaches 2. This problem covers important calculus concepts such as limits, polynomial functions, and continuity. Ideal for students in Grades 10-12.

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