https://file.aiquickdraw.com/mathbot/file/17410080759175y9u5n2d.jpg

The image you uploaded shows a limit expression for a trigonometric function:

\[
\lim_{x \to 0} \frac{\sin x}{x}
\]

This is a well-known limit that evaluates to 1. The limit:

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

This result is important in calculus and can be derived using L'Hopital's Rule, series expansion, or geometric reasoning.

Would you like more details on how to derive this result, or any specific explanation related to this? Let me know!

Here are a few questions you could explore:
1. How can L'Hopital's Rule be used to evaluate this limit?
2. What is the significance of the result \(\lim_{x \to 0} \frac{\sin x}{x} = 1\) in calculus?
3. How does the small angle approximation of \(\sin x\) help in evaluating the limit?
4. What are other trigonometric limits that are commonly used in calculus?
5. How can we use this limit to evaluate limits of other trigonometric functions?

**Tip:** Whenever you encounter indeterminate forms like \(\frac{0}{0}\), L'Hopital's Rule or series expansion can often simplify the problem.

Evaluate the limit: lim (x -> 0) sin(x)/x

Learn how to evaluate the limit lim (x -> 0) sin(x)/x, which equals 1. This limit is essential in calculus and can be derived using L'Hopital's Rule, small angle approximation, or geometric reasoning. Ideal for students in Grades 11-12.

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