Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)lim h → 0 9 + h − 3h

1. Break Down the Problem

We want to evaluate the limit as $h$ approaches $0$ for the expression $9 + h - 3h$. This can be simplified before finding the limit.

2. Relevant Concepts

To find $\lim_{h \to 0}(9 + h - 3h)$, we combine like terms. Limits can often be calculated by substituting the value directly if the expression is continuous at that point.

3. Analysis and Detail

Let's simplify the expression: $9 + h - 3h = 9 + (1 - 3)h = 9 - 2h$

Now we need to evaluate the limit: $\lim_{h \to 0}(9 - 2h)$

Substituting $h = 0$: $9 - 2(0) = 9$

4. Verify and Summarize

We have simplified the expression correctly and substituted $h$ with $0$, resulting in $9$. The limit exists as the expression is continuous.

Final Answer

$\lim_{h \to 0}(9 + h - 3h) = 9$