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

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The limit of (5x)/(100 - x) as x approaches 100 from the left is discussed, with the side condition that x must be less than 100. Initial calculations suggested negative infinity, but the correct limit is positive infinity, as confirmed by the textbook. The confusion arises from the behavior of the function as x nears 100, where the denominator approaches zero positively while the numerator remains positive. A graphing tool like Desmos is recommended to visualize this limit more clearly. The discussion emphasizes the importance of careful evaluation in limit problems.
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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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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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