Here is a table of values for the function 𝑓(𝑥)=ln(𝑥−1)/2𝑥−4.

Question

Here is a table of values for the function 𝑓(𝑥)=ln(𝑥−1)/2𝑥−4.

𝑥	𝑓(𝑥)
1.9	0.526803
1.99	0.502517
1.999	0.50025
1.9999	0.500025
2.0001	0.49975
2.001	0.49975
2.01	0.497517
2.1	0,476551

Based on the table, it seems like lim𝑥→2𝑓(𝑥)=?

0

1/2

does not exist.

2

2^1/2

Answer 1

This should be an easy multiple choice. Just look at the values of 𝑓(𝑥) when 𝑥 is really close to 2.

Although you're not asked to, you can calculate the indicated limit using L'Hôpital's rule if you know that the derivative of ln(𝑥−1) is equal to 1/(𝑥−1).