https://file.aiquickdraw.com/mathbot/file/17259463765671h7j75de.jpg

I can see the image with a set of limits to evaluate. Here is a transcription of the limits shown:

1. \[
\lim_{x \to 0} \frac{\sin^2{x}}{x^2}
\]
2. \[
\lim_{t \to 3} \frac{\sin(t - 3)}{t - 3}
\]
3. \[
\lim_{t \to 2} \frac{1 - \cos(t - 2)}{t - 2}
\]
4. \[
\lim_{t \to 3} e^{t - 3} - 1
\]
5. \[
\lim_{x \to 1} \frac{x^2 - 1}{x + 1}
\]

Would you like me to start solving these problems one by one or any specific one in particular? Let me know if you need any clarifications!

Here are some follow-up questions for your understanding:
1. What is the general method for evaluating limits involving trigonometric functions?
2. How can you use L'Hopital's Rule to solve indeterminate forms?
3. What does it mean when a limit approaches infinity or a specific point?
4. What are the key techniques for simplifying complex limit expressions?
5. How do you identify when to factor or use trigonometric identities to solve limits?

**Tip:** When you encounter limits that result in an indeterminate form like \( \frac{0}{0} \), try applying L'Hopital's Rule or simplifying the expression through factoring or using known limit properties.

Evaluate the following limits: 1. lim (x -> 0) sin^2(x) / x^2, 2. lim (t -> 3) sin(t - 3) / (t - 3), 3. lim (t -> 2) (1 - cos(t - 2)) / (t - 2), 4. lim (t -> 3) e^(t - 3) - 1, 5. lim (x -> 1) (x^2 - 1) / (x + 1)

This page provides detailed solutions for evaluating limits involving trigonometric functions, exponential expressions, and algebraic identities. The problems involve the application of L'Hopital's Rule and standard limit properties, suitable for advanced high school or early college students.

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