https://file.aiquickdraw.com/mathbot/file/1727361305916bffjrn0h.jpg

The image shows the following mathematical expression:

\[
\lim_{h \to 0} \frac{3h}{h + 1}
\]

To find the limit of this expression as \( h \to 0 \), let's break it down:

1. **Substitute \( h = 0 \) directly** into the expression:

\[
\frac{3h}{h + 1} = \frac{3(0)}{0 + 1} = \frac{0}{1} = 0
\]

Therefore, the limit is:

\[
\lim_{h \to 0} \frac{3h}{h + 1} = 0
\]

Would you like more details on limits or explanations? Let me know!

### Related Questions:
1. What is the general rule for calculating limits when both the numerator and denominator approach zero?
2. How do you handle indeterminate forms in limits?
3. What is L'Hopital's Rule, and how can it help in limit problems?
4. Can this type of limit be solved using algebraic simplifications?
5. How do limits relate to the concept of continuity in calculus?

#### Tip:
When approaching limit problems, always check if direct substitution gives a valid result before applying more advanced techniques like factorization or L'Hopital's Rule.

Learn how to find the limit of the expression \lim_{h \to 0} \frac{3h}{h + 1}. This problem covers limits and algebraic concepts suitable for high school students (Grades 10-12).

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