Evaluate the limit as x approaches 3 for the function f(x).
Understand the Problem
The question appears to involve the concept of a mathematical limit or a statement about a limit involving variables. It is likely asking for an evaluation or analysis of a limit as the variables approach certain values.
Answer
The limit is $6$.
Answer for screen readers
The limit as ( x ) approaches 3 for the function ( f(x) ) is 6.
Steps to Solve

Identify the function The function given in the limit is ( f(x) = \frac{x^2  9}{x  3} ).

Factor the numerator We can factor ( x^2  9 ) as a difference of squares: $$ x^2  9 = (x  3)(x + 3) $$

Rewrite the function Now, substitute the factored form back into the function: $$ f(x) = \frac{(x  3)(x + 3)}{x  3} $$

Simplify the function For ( x \neq 3 ), ( (x  3) ) cancels out: $$ f(x) = x + 3 $$

Evaluate the limit Now, evaluate the limit as ( x ) approaches 3: $$ \lim_{x \to 3} f(x) = \lim_{x \to 3} (x + 3) = 3 + 3 = 6 $$
The limit as ( x ) approaches 3 for the function ( f(x) ) is 6.
More Information
This limit is an example of applying algebraic simplification to evaluate a limit at a point where the function is initially undefined. The process of factoring and canceling terms is a common technique in limit evaluation.
Tips
 Ignoring cancellation: Sometimes students forget to cancel terms correctly, leading to incorrect conclusions about the limit.
 Substituting directly into a form like ( \frac{0}{0} ): The limit must be simplified before direct substitution.