MHB Finding the Limit of an Arctan Equation

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To find the limit of arctan(3/(x-2) as x approaches 2 from the left, it's important to recognize that as x approaches 2, the expression 3/(x-2) approaches negative infinity. This results in the arctan function approaching -π/2, since arctan of negative infinity equals -π/2. The discussion highlights initial confusion about how to approach the limit and the relevance of rewriting the equation. Ultimately, the limit is determined to be -π/2. Understanding the behavior of the arctan function near its asymptotes is crucial for solving similar problems.
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The Question
Find the limit as x approaches 2 from the left for the equation
arctan(3/(x-2))
Work Done
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.
 
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I would begin with the fact that given a one-to-one function $f$, we may state:

$$\lim_{x\to a}\left(f\left(u(x) \right) \right)=f\left(\lim_{x\to a}\left(u(x) \right) \right)$$
 
Thanks, I managed to figure it out though.
 
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