Evaluate: limx→4x−44−x
 A. Does not exist
 B. -4
 C. -1
 D. 0

To evaluate the limit \(\lim_{x \to 4} \frac{x - 4}{4 - x}\), let's first simplify the expression:

\[
\lim_{x \to 4} \frac{x - 4}{4 - x}
\]

Notice that the numerator \(x - 4\) and the denominator \(4 - x\) are negatives of each other. Specifically:

\[
x - 4 = -(4 - x)
\]

So the expression can be rewritten as:

\[
\lim_{x \to 4} \frac{-(4 - x)}{4 - x} = \lim_{x \to 4} -1
\]

Since \(-1\) is a constant, the limit is simply:

\[
\lim_{x \to 4} -1 = -1
\]

Thus, the correct answer is:

**C. -1**

Would you like further details on this topic, or do you have any other questions?

Here are some related questions:
1. How do you evaluate the limit when \( x \) approaches infinity?
2. What are one-sided limits, and how do they differ from two-sided limits?
3. Can a limit exist if the left-hand limit and the right-hand limit are different?
4. How does L'Hôpital's Rule apply to limits involving indeterminate forms?
5. What is the limit definition of a derivative?
6. How do you determine if a function is continuous at a point using limits?
7. What are infinite limits and how are they evaluated?
8. How do you apply the squeeze theorem to evaluate limits?

**Tip:** When dealing with limits that involve fractions, always check if you can simplify the expression by factoring or by recognizing patterns, like the one in this problem.

Learn how to evaluate the limit as x approaches 4 of (x - 4) / (4 - x). Follow a step-by-step solution to simplify the expression and determine the correct answer. Suitable for students in Grades 11-12 studying limits and algebraic expressions.

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