To evaluate the limit as h approaches 0 for the expression √(9h + 3h), we start by simplifying the expression inside the square root.
1. **Combine the terms:** The expression can be rewritten as:
√(9h + 3h) = √(12h)
2. **Substituting h = 0:** Now, we replace h with 0 to see how the expression behaves:
√(12(0)) = √(0) = 0
3. **Analyzing the limit:** Thus, as h approaches 0, the limit of the entire function converges to:
lim (h -> 0) √(12h) = 0
In conclusion, the evaluated limit of the expression as h approaches 0 is 0.