Question

Estimate the limit lim(x→5) -6x² - 25x numerically or state that the limit does not exist.

a) 125
b) 95
c) 70
d) The limit does not exist

Answer 1

The estimated limit for the function -6x² - 25x as x approaches 5 is -275. Direct substitution into the function was used for the calculation, and the answer does not match any of the provided options, indicating a possible typo or mistake in the question.

Step-by-step explanation:

To estimate the limit of a function as x approaches a certain value, we can simply plug that value into the function if it is within the domain and the function is continuous at that point. This question asks for the limit of the function -6x² - 25x as x approaches 5. Using direct substitution, we calculate:

Step-by-Step Calculation:

1. Plug x = 5 into the function: -6(5)² - 25(5).
2. Calculate the square of 5, which is 25, and multiply by -6 to get -150.
3. Multiply 25 by -25 to get -125.
4. Add the two results together: -150 - 125 = -275.

So, the estimated limit is -275, which is not among the answer choices provided. Therefore, it looks like there may have been a typo or mistake in the answer choices or the function itself.