# What is the Limit of (5x)/(100 - x) as x Approaches 100 from the Left?

• MHB
In summary, the conversation is about finding the limit of (5x)/(100 - x) as x approaches 100 from the left side. The textbook answer is positive infinity, but the person asking the question got negative infinity when creating a table of values slightly less than 100. They ask for help using Desmos to graph the function and find the limit from the graph. The other person responds with a link to the graph and suggests looking at the table again, since for values close to 100, 100 - x is close to 0 and positive while 5x is positive. The conversation ends with the first person realizing they need to slow down when answering questions.
Find the limit of (5x)/(100 - x) as x tends to 100 from the left side.

The side condition given: 0 <= x < 100

To create a table, I must select values of x slightly less than 100.
I did that and ended up with negative infinity as the answer. The textbook answer is positive infinity.

Can you please use Desmos to show the graph? This will allow me to find the limit from the graph of the function.

Beer soaked ramblings follow.
...
Can you please use Desmos to show the graph? This will allow me to find the limit from the graph of the function.
Problem 1.5.77.
https://www.desmos.com/calculator/ojcgjmr8t6

Beer soaked query follows.
...
To create a table, I must select values of x slightly less than 100.
I did that and ended up with negative infinity as the answer. The textbook answer is positive infinity.
...
Can you show how you did something so seemingly impossible?

For x close to 100 but close to 100, 100- x is close to 0 and positive while 5x is positive. Look at your table again!

Country Boy said:
For x close to 100 but close to 100, 100- x is close to 0 and positive while 5x is positive. Look at your table again!

I got to stop rushing through questions.

## 1. What is a rational function?

A rational function is a mathematical function that can be expressed as a ratio of two polynomial functions. It can be written in the form of f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions 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 independent variable (usually denoted as x) gets closer and closer to a certain value. This value is also known as the limit point or the point of convergence.

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

To find the limit of a rational function, you can use algebraic manipulation, substitution, or graphing. The most common method is to use algebraic manipulation, which involves simplifying the function by factoring and canceling out common terms until you can directly substitute the limit point into the simplified function.

## 4. What are the conditions for a rational function to have a limit?

A rational function will have a limit if the denominator does not equal 0 at the limit point and the numerator and denominator do not both approach 0 at the same time. This is known as the "indeterminate form" and requires further manipulation or use of other methods to find the limit.

## 5. Why is the limit of a rational function important?

The limit of a rational function is important because it helps us understand the behavior of the function at a specific point. It can also help us determine the behavior of the function as x approaches positive or negative infinity. Limits are used in many areas of mathematics, such as calculus, to solve problems and make predictions.

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