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1. A limit problem: $\lim_{{x \to 0}} \frac{\sin(x)}{x}$

This is a well-known limit in calculus, and the result is: $\lim_{{x \to 0}} \frac{\sin(x)}{x} = 1$

Would you like further clarification or details on this? Here are some related questions to consider:

1. What are the general steps for solving limits involving trigonometric functions?
2. How can L'Hôpital's Rule be applied to similar indeterminate forms?
3. What is the graphical interpretation of $\lim_{{x \to 0}} \frac{\sin(x)}{x}$?
4. Are there other limits involving trigonometric functions that are important to know?
5. How can Taylor series expansions help with finding limits?

Tip: When dealing with limits that yield an indeterminate form, consider using algebraic manipulation or L'Hôpital's Rule for simplification.