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

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Discussion Overview

The discussion centers on finding the limit of the function (5x)/(100 - x) as x approaches 100 from the left. Participants explore the implications of this limit, including the behavior of the function near the point of interest and the discrepancies between personal calculations and textbook answers.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant reports calculating the limit as negative infinity when selecting values of x slightly less than 100, while the textbook states it should be positive infinity.
  • Another participant suggests using Desmos to graph the function to visualize the limit behavior.
  • Several participants emphasize that as x approaches 100 from the left, the term (100 - x) approaches 0 and remains positive, while (5x) remains positive, indicating a potential oversight in the initial calculations.
  • One participant expresses a desire for clarification on how the conflicting results were obtained.

Areas of Agreement / Disagreement

Participants express disagreement regarding the limit's value, with some asserting it approaches positive infinity and others claiming it approaches negative infinity based on their calculations.

Contextual Notes

Participants mention the importance of selecting appropriate values for x and the implications of the function's behavior near the limit point, but do not resolve the discrepancies in their findings.

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

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