Limit of Rational Function....1

In summary, the conversation discusses finding the limit of a function as x approaches 2 from the left side. Using a table and understanding the behavior of the numerator and denominator, it is determined that the limit is negative infinity. The conversation also briefly mentions flattering someone in hopes of getting them to do more math problems.
  • #1
nycmathdad
74
0
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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  • #2
Problem 1.5.27.
Odd numbered.
Look up the answer.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
Blush
(Saying I am "good at math" because I can do high school algebra is hardly flattering!)
 
Last edited:

1. What is a rational function?

A rational function is a mathematical function that can be expressed as a ratio of two polynomials. It can be written in the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) is not equal to 0.

2. What is the limit of a rational function?

The limit of a rational function is the value that the function approaches as the input variable (usually denoted as x) approaches a certain value. This value can be found by plugging in the input value into the function and simplifying the resulting expression.

3. How do you determine the limit of a rational function?

To determine the limit of a rational function, you can use the rules of limits such as direct substitution, factoring, and cancelling common factors. If these methods do not work, you can use L'Hôpital's rule or graph the function to estimate the limit.

4. What is the difference between a finite and infinite limit of a rational function?

A finite limit of a rational function means that the function approaches a specific value as the input variable approaches a certain value. An infinite limit means that the function either approaches positive or negative infinity as the input variable approaches a certain value.

5. Why are limits of rational functions important?

Limits of rational functions are important because they help us understand the behavior of a function near a certain input value. They also allow us to find the maximum or minimum value of a function, identify asymptotes, and solve real-world problems involving rates of change.

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