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.