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The limit of the expression \(\lim_{{x \to 0}} \frac{{\sin(3x) + \sin(2x)}}{{5x}}\) is \(1\).

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Here are some related questions:
1. How do you find limits involving trigonometric functions?
2. What is L'Hôpital's rule, and how can it be applied to limits like this?
3. How does the small-angle approximation for sine function help in limit problems?
4. Can the limit of a sum be split into individual limits?
5. How would the limit change if we had \(\cos(3x)\) instead of \(\sin(3x)\)?

**Tip:** The small-angle approximation \(\sin(x) \approx x\) for small values of \(x\) is often useful in limit problems.

lim(x → 0) (sin(3x) + sin(2x)) / (5x) =

Learn how to solve the limit problem lim(x → 0) (sin(3x) + sin(2x)) / (5x). This problem covers trigonometric functions, small angle approximations, and uses basic calculus techniques like L'Hôpital's Rule. Ideal for students in Grades 11-12.

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