https://file.aiquickdraw.com/mathbot/file/1725412837678o0jnupth.jpg

The image shows the following limit problem:

\[
\text{a. } \lim_{x \to 1} \frac{x^2 + 2x - 3}{2x - 3}
\]

Let's solve this limit step by step.

### Step 1: Direct Substitution
First, we try to directly substitute \(x = 1\) into the expression.

\[
\frac{(1)^2 + 2(1) - 3}{2(1) - 3} = \frac{1 + 2 - 3}{2 - 3} = \frac{0}{-1} = 0
\]

### Step 2: Analyze the Result
Since direct substitution gives us a defined value (0), the limit exists and is equal to 0.

Thus, the solution is:

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

Would you like more details, or do you have any questions?

Here are five related questions:
1. How do you solve limits that involve indeterminate forms like \( \frac{0}{0} \)?
2. What are some techniques for simplifying complex limit expressions?
3. Can L'Hôpital's Rule be applied to this problem?
4. How do you determine if a limit does not exist?
5. What is the significance of limits in calculus?

**Tip:** When you substitute a value into a limit and get \( \frac{0}{0} \), you often need to factor and simplify the expression before taking the limit again.

The limit problem: lim(x→1) [(x^2 + 2x - 3) / (2x - 3)]

Learn how to solve the limit problem lim(x→1) [(x^2 + 2x - 3) / (2x - 3)] using direct substitution. This problem covers important calculus concepts and is suitable for students in Grades 10-12.

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