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

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SUMMARY

The limit of the function (5x)/(100 - x) as x approaches 100 from the left is positive infinity. This conclusion is reached by analyzing the behavior of the function as x gets closer to 100, where the denominator (100 - x) approaches zero while remaining positive, and the numerator (5x) remains positive. A common misconception is that the limit approaches negative infinity; however, the correct interpretation confirms that the limit is indeed positive infinity. Utilizing graphing tools like Desmos can aid in visualizing this limit effectively.

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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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