MHB What is the Limit of (3x)/(x-2) as x Approaches 2 from the Left?

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Find the limit of (3x)/(x - 2) as x tends to 2 from the left side.

Approaching 2 from the left means that the values of x must be slightly less than 2.

I created a table for x and f(x).

x...0...0.5...1...1.5
f(x)...0...-1...-3...-9

I can see that f(x) is getting smaller and smaller and possibly without bound.

I say the limit is negative infinity.

Yes?
 
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Problem 1.5.27.
Odd numbered.
Look up the answer.
 
For x close to 2 but less than 2, the denominator, x- 2 is close to 0 and negative while the numerator, 3x, is close to 6 and positive. That is enough to say that, for x going to 2 from the left, the fraction goes to negative infinity.
 
Country Boy said:
For x close to 2 but less than 2, the denominator, x- 2 is close to 0 and negative while the numerator, 3x, is close to 6 and positive. That is enough to say that, for x going to 2 from the left, the fraction goes to negative infinity.

You are good in math.
 
Beer soaked ramblings follow.
nycmathdad said:
You are good in math.
Translation: I hope flattering him would induce him to do more of my math problems for me.
 
Blush
(Saying I am "good at math" because I can do high school algebra is hardly flattering!)
 
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