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The problem you have uploaded is asking to find the limit:

\[
\lim_{h \to 0} \frac{(7 + 2h) - 7}{h}
\]

### Step-by-Step Solution:

1. **Simplify the expression** in the numerator:
   \[
   (7 + 2h) - 7 = 2h
   \]
   So the expression becomes:
   \[
   \lim_{h \to 0} \frac{2h}{h}
   \]

2. **Simplify the fraction**:
   \[
   \frac{2h}{h} = 2 \quad (\text{as long as } h \neq 0)
   \]

3. **Take the limit** as \( h \to 0 \):
   \[
   \lim_{h \to 0} 2 = 2
   \]

Thus, the limit is \( \boxed{2} \).

Would you like further details or have any questions?

### Related Questions:
1. What are the conditions under which \( \frac{h}{h} = 1 \)?
2. How would the answer change if the expression in the numerator were \( (7 + 3h) - 7 \)?
3. How does this limit relate to the concept of derivatives?
4. What happens to the limit if we modify the expression to include \( h^2 \)?
5. Can L'Hôpital's Rule be applied here?

**Tip:** Always simplify the expression before taking the limit to avoid unnecessary complications.

Find the limit by simplifying the expression: lim(h -> 0) [(7 + 2h) - 7] / h

Learn how to calculate the limit lim(h -> 0) [(7 + 2h) - 7] / h with a step-by-step simplification process. This problem is ideal for students learning the fundamentals of calculus and limit operations. Suitable for Grades 10-12.

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