Question

evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim x→−9 2x² 17x − 9 x² − 81

Answer 1

To find the limit as x approaches -9 for the given function, substitute -9 into the function and simplify. The limit does not exist (DNE).

Step-by-step explanation:

To evaluate the limit as x approaches -9 for the given function, we need to substitute -9 into the function and simplify.

1. Replace x with -9 in both the numerator and denominator: (2(-9)² + 17(-9) - 9) / ((-9)² - 81)
2. Simplify the numerator and denominator: (-162 + (-153) - 9) / (81 - 81)
3. Continue simplifying: (-324) / 0

The result is -324 divided by 0, which is undefined. Therefore, the limit does not exist (DNE).