To evaluate the limit lim h → 0 √(9h) / (3h), we can start by simplifying the expression.
First, we note that the square root term can be simplified:
- √(9h) can be rewritten as √9 * √h = 3√h.
Now, we can rewrite the limit:
lim h → 0 (3√h) / (3h) = lim h → 0 √h / h.
Next, we can simplify this further:
- √h / h = 1 / √h.
Now, we have to evaluate the limit:
lim h → 0 (1 / √h).
As h approaches 0, √h also approaches 0, which means that 1 / √h approaches infinity.
Therefore, the limit is:
∞ (infinity).