https://r2.erweima.ai/mathbot/image/17272197088083c2d8jmk.jpg

The problem in the image asks to evaluate the following limit:

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

To solve it, we substitute \(x = -5\) directly into the expression \(x^2 - 3x + 4\), since it's a polynomial function and continuous for all \(x\).

Let's calculate the limit step-by-step:

1. Substitute \(x = -5\) into the expression:
\[
(-5)^2 - 3(-5) + 4
\]

2. Compute each term:
\[
(-5)^2 = 25
\]
\[
-3(-5) = 15
\]
\[
4 = 4
\]

3. Add the terms:
\[
25 + 15 + 4 = 44
\]

Thus, the limit is \(44\). Therefore, the correct answer is:

**b. 44**

Would you like more details or further explanation? Here are some related questions to consider:

1. What are the steps to solve a limit involving a rational function?
2. How do you handle limits involving indeterminate forms like \( \frac{0}{0} \)?
3. What is the definition of a continuous function?
4. How would you solve a limit as \( x \to \infty \)?
5. Can you apply L'Hopital's Rule in this limit?

**Tip**: Polynomials are continuous everywhere, so you can directly substitute the value of \(x\) when evaluating limits for them!

Hallar el siguiente límite: lim(x → -5) (x^2 − 3x + 4)

Solve the limit lim(x → -5) (x^2 − 3x + 4) by substituting x = -5 into the polynomial expression. This problem covers key concepts of limits and polynomials, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation