https://file.aiquickdraw.com/mathbot/file/1727057281664ngq3vhdm.jpg

Let's solve the limit problem provided in the image:

We are asked to compute the following limit:

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

### Step-by-step solution:

1. **Substitute the value of \( x = 1 \) into the function**:
   Since this is a polynomial, and polynomials are continuous, we can directly substitute \( x = 1 \) into the expression \( x^2 + 3x - 4 \).

   Substituting \( x = 1 \):

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

2. **Conclusion**:
   The limit evaluates to \( 0 \).

Thus, the final answer is:

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

Would you like further clarification on any of these steps?

Here are 5 related questions for practice:
1. What is \( \lim_{{x \to 2}} (x^2 + 3x - 4) \)?
2. How would you solve \( \lim_{{x \to 1}} (2x^2 - 5x + 3) \)?
3. What is the limit of \( \lim_{{x \to -1}} (x^2 + 3x - 4) \)?
4. Can you evaluate \( \lim_{{x \to 1}} \frac{x^2 + 3x - 4}{x - 1} \)?
5. How does the substitution method work for other types of functions, such as rational or trigonometric functions?

**Tip**: For polynomial functions, direct substitution is a valid and effective method for finding limits, since polynomials are continuous over all real numbers.

Apply the limit rules to find lim_{x→1} (x^2 + 3x - 4) and explain your steps.

Learn how to solve the limit problem lim_{x→1} (x^2 + 3x - 4) using direct substitution. This step-by-step guide explains how to evaluate limits of polynomial functions and demonstrates the application of limit rules. Suitable for high school calculus students.

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