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?
Captain Matticus, LandPiratesInc
Favorite 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.
llaffer
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)