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

[nycmathdad]

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?

 

[jonah1]

Problem 1.5.27.
Odd numbered.
Look up the answer.

 

[HOI]

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.

 

[nycmathdad]

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.

 

[jonah1]

Beer soaked ramblings follow.

You are good in math.

Translation: I hope flattering him would induce him to do more of my math problems for me.

 

[HOI]

Blush
(Saying I am "good at math" because I can do high school algebra is hardly flattering!)