Question

Find the limit as x approaches 2 from the left for the equation
arctan(3/(x-2))

Answer 1

I'm not really sure even where to start. My teacher didn't go over this type of question. I don't see any way to mess with the equation to make it so we can plug in 2, and I don't see how rewriting the equation in the form tan y = 3/(x-2) could help either. I'm not supposed to take the derivative, am I?
I would appreciate any pushes in the right direction.

Answer 2

as x->2-, what happens to x-2?

Answer 3

x-2 approaches 0?

Answer 4

correct. But specifically, is x-2 positive or negative?

Answer 5

It's negative.

Answer 6

ok, so if denominator keeps getting smaller and smaller negatively, what happens to the value of 3/(x-2) ?

Answer 7

It approaches negative infinity.

Answer 8

excellent. What do you know about arctan(u) as u approaches negative infinity?

Answer 9

It approaches -pi/2 - OHHH okay I get it now

Answer 10

good