Final answer:
After factoring and simplifying the expression, the limit of (x² - 3x - 4)/(x - 4) as x approaches 4 is found to be 5. This shows that the limit does exist and the answer is not among the provided options.
Step-by-step explanation:
To evaluate the limit lim(x → 4) (x² - 3x - 4)/(x - 4), we first try to simplify the expression by factoring the numerator (if possible) to see if it can cancel any factors from the denominator. In this case, the numerator factors to (x-4)(x+1). Therefore, the equation becomes:
(x - 4)(x + 1) / (x - 4)
Since x is approaching 4 but is not equal to 4, we can cancel out the (x-4) terms, leaving us with:
x + 1
We then evaluate this at the point x = 4:
4 + 1 = 5
This gives us the limit value as x approaches 4. So the correct answer is 5, which is not among the provided choices (A, B, C, D), indicating there may have been a mistake in the options listed. The limit exists and is equal to 5.