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The given expression is:

\[
\lim_{{h \to 0}} \frac{h}{\sin(3h)}
\]

To solve this limit, we can use the well-known limit property:

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

We can adjust the argument inside the sine function to use this property. Here's the step-by-step process:

1. Rewrite the expression:
   \[
   \lim_{{h \to 0}} \frac{h}{\sin(3h)}
   \]

2. Factor out the constant from the argument of the sine:
   \[
   \lim_{{h \to 0}} \frac{1}{3} \cdot \frac{3h}{\sin(3h)}
   \]

3. Now apply the limit:
   \[
   \lim_{{h \to 0}} \frac{3h}{\sin(3h)} = 1
   \]

4. Therefore, the entire expression becomes:
   \[
   \frac{1}{3} \cdot 1 = \frac{1}{3}
   \]

So, the value of the limit is:

\[
\lim_{{h \to 0}} \frac{h}{\sin(3h)} = \frac{1}{3}
\]

Would you like more details or further clarifications?

Here are some related questions for further practice:
1. What is \(\lim_{{x \to 0}} \frac{\sin(5x)}{x}\)?
2. How does the limit \(\lim_{{h \to 0}} \frac{\tan(h)}{h}\) behave?
3. Can you evaluate \(\lim_{{h \to 0}} \frac{\sin(h)}{h}\) using L'Hopital's Rule?
4. What is \(\lim_{{x \to 0}} \frac{h^2}{\sin(h)}\)?
5. How do you calculate \(\lim_{{x \to 0}} \frac{\sin^2(x)}{x^2}\)?

**Tip:** When dealing with limits of trigonometric functions, remember the fundamental limits like \(\lim_{{x \to 0}} \frac{\sin(x)}{x} = 1\), which are very useful in simplifications!

Learn how to solve the limit problem lim (h -> 0) (h / sin(3h)) using the fundamental limit property lim (x -> 0) (x / sin(x)) = 1. This problem involves trigonometric limits and is suitable for students in Grades 11-12.

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