Question

How do you find the limit `lim_(x->2^-)1/(x-2)`?

Answer 1

negative infinity

Explanation:

as x goes to 2 from below - so imagine a number just a tiny bit LESS than 2.

This number minus 2 gives a remainder that is a very tiny negative number.

1 divided by a negative number is negative, and one divided by a tiny negative number is a very large negative number.

So you can say that the function tends to negative infinity as x approaches 2 from below. (or from the left)

It's often good to have a graph of the function as a sanity check...

graph{1/(x-2) [-10, 10, -5, 5]}