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resolva a questao da imagem e assinale a alternativa correta

Let's analyze and solve the problem shown in the image.

The problem appears to involve limits, and the main expression given is:

\[
\lim_{{x \to 3}} \frac{{5x - 15}}{{x - 3}}
\]

We need to determine the correct answer from the options provided. 

### Solution

First, let's simplify the expression inside the limit:

\[
\frac{{5x - 15}}{{x - 3}}
\]

Notice that the numerator can be factored:

\[
5x - 15 = 5(x - 3)
\]

So the expression becomes:

\[
\frac{{5(x - 3)}}{{x - 3}}
\]

For \(x \neq 3\), the \((x - 3)\) terms cancel out, leaving:

\[
\lim_{{x \to 3}} 5 = 5
\]

Thus, the limit is 5.

### Correct Option
From the options in the image, the correct one is:

**Option C: 5**

Would you like further details or have any additional questions? 

Here are five related questions you might find useful:

1. What is the difference between one-sided and two-sided limits?
2. How do you apply L'Hôpital's Rule to solve limits that result in indeterminate forms?
3. Can a function have different limits from the left and the right at a certain point?
4. What is the geometric interpretation of limits in calculus?
5. How does factoring help in solving limit problems involving rational functions?

**Tip:** Always check if you can factor expressions in the limit to simplify your calculations before applying other limit-solving techniques.

Learn how to solve the limit problem: lim(x -> 3) (5x - 15) / (x - 3). Detailed step-by-step solution involving limits, rational functions, and factorization techniques. Suitable for college-level calculus students.

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