Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Limit of Rational Function...3?
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. How is this done?
2 Answers
- 4 days agoFavorite Answer
Change the parameters
u = 100 - x
x = 100 - u
5x / (100 - x) =>
5 * (100 - u) / u =>
5 * (100/u - u/u) =>
5 * (100/u - 1) =>
500/u - 5
0 </= x < 100
0 </= 100 - u < 100
-100 </= -u < 0
0 < u </= 100
Notice that as u goes to 0, 500/u tends to positive infinity.
I don't know how you got negative infinity, to be honest, since 100 - x will always be positive when x is between 0 and 100 and 5 * x will be positive as well.
x = 99.99
5 * 99.99 / (100 - 99.99) =>
5 * 99.99 / 0.01 =>
5 * 9999 =>
49995
x = 99.999
5 * 99.999 / (100 - 99.999) =>
5 * 99.999 / 0.001 =>
5 * 99999 =>
499995
And so on.
- llafferLv 74 days ago
You'd have negative if you went over 100. I'll do this with 99.999:
(5x) / (100 - x)
(5 * 99.999) / (100 - 99.999)
499.995 / 0.001
499995
That's a large number (huge compared to the 100), the closer I get to 100 and higher it will get, so it's positive infinity from the left (when x < 100).
And as you found out, it's negative infinity from the right (when x > 100)
