It looks like you want to evaluate the limit of an expression involving trigonometric functions. I assume your expression is:

\[
\lim_{x \to 0} \frac{\sin^2(x)}{x^2}
\]

Let’s break this down:

We can use the known limit:

\[
\lim_{x \to 0} \frac{\sin(x)}{x} = 1
\]

This means that:

\[
\lim_{x \to 0} \frac{\sin^2(x)}{x^2} = \left(\lim_{x \to 0} \frac{\sin(x)}{x}\right)^2 = 1^2 = 1
\]

Thus, the limit is:

\[
\boxed{1}
\]

Do you want more details or have any other questions?

Here are five related questions:
1. How do you evaluate limits of trigonometric functions as \( x \to \infty \)?
2. What is the limit of \(\frac{\sin(x)}{x}\) as \(x\) approaches infinity?
3. How do you evaluate limits involving \(\tan(x)\) or \(\cos(x)\)?
4. How do you apply L'Hopital's Rule to limits like this?
5. How would this change if \(\sin^2(x)\) was replaced by \(\cos^2(x)\)?

**Tip:** Memorizing common trigonometric limits, like \(\lim_{x \to 0} \frac{\sin(x)}{x} = 1\), can make solving limit problems faster and easier!

Learn how to evaluate the limit of (sin^2(x)/x^2) as x approaches 0 using the trigonometric limit theorem. This step-by-step solution breaks down key concepts in calculus and provides useful tips for solving similar trigonometric limit problems. Suitable for students in Grades 11-12.

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