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The image you uploaded contains several limit problems. Let's go through them one by one.

### Problem 1:
\[
\lim_{x \to 3} \left(x^2 - 13\right)
\]
This is a direct substitution problem. Substitute \(x = 3\):
\[
3^2 - 13 = 9 - 13 = -4
\]
So, the answer is:
\[
\boxed{-4}
\]

### Problem 2:
\[
\lim_{x \to 2} \left(x^3 - 2x^2 + 4x + 8\right)
\]
Substitute \(x = 2\):
\[
2^3 - 2(2^2) + 4(2) + 8 = 8 - 8 + 8 + 8 = 16
\]
Thus, the answer is:
\[
\boxed{16}
\]

### Problem 3:
\[
\lim_{s \to 7/3} \left(8 - 3s\right)(2s - 1)
\]
Substitute \(s = \frac{7}{3}\):
\[
\left(8 - 3\left(\frac{7}{3}\right)\right)\left(2\left(\frac{7}{3}\right) - 1\right) = \left(8 - 7\right)\left(\frac{14}{3} - 1\right) = 1\left(\frac{14}{3} - \frac{3}{3}\right) = \frac{11}{3}
\]
So, the answer is:
\[
\boxed{\frac{11}{3}}
\]

### Problem 4:
\[
\lim_{h \to 2} \left(h^2 + 5h - 2\right)
\]
Substitute \(h = 2\):
\[
2^2 + 5(2) - 2 = 4 + 10 - 2 = 12
\]
Thus, the answer is:
\[
\boxed{12}
\]

### Problem 5:
\[
\lim_{x \to 2} \left(x^2 - 4\right)
\]
Substitute \(x = 2\):
\[
2^2 - 4 = 4 - 4 = 0
\]
The answer is:
\[
\boxed{0}
\]

### Would you like to continue with the other problems? Let me know if you want further details on any step.

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### Here are some related questions:
1. How do you solve limits that result in indeterminate forms like \( \frac{0}{0} \)?
2. What is the difference between one-sided and two-sided limits?
3. How can L'Hopital's rule help with solving more complex limit problems?
4. What are some common techniques for solving polynomial limits?
5. How do you compute limits involving trigonometric functions?

#### Tip: When direct substitution in a limit gives \( \frac{0}{0} \), try factoring or applying L'Hopital's rule to resolve the indeterminate form.

Solve the limit problems listed on the whiteboard.

Explore solutions for a set of limit problems including substitution, factoring, and indeterminate forms. These problems help students understand key concepts in calculus, such as direct substitution and applying limit laws. Suitable for Grades 11-12 calculus students.

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