I just thought about this. Stupid question some would say; a brain killer to others.
The graph of x/x should be similar to the graph of 1, but since there's a variable in the denominator, then the domain for x/x is all real numbers except x=0.
Therefore, there is a 'hole' at x=0 on the graph of x/x, whereas the graph of 1 is continuous everywhere. Now, it is said that anything divided by itself is equal to one, but how about the case of x/x?
If you simplify x/x, it would be equal to one, but by leaving it as is, it isn't quite the same.
Anyhow, just a matter I thought would be interesting to point out.
And no, I'm not on crack, thank you.
2007-09-24 19:06:01 · 6 answers · asked by J. Morrissey 2 in Science & Mathematics ➔ Mathematics
Beautiful. Answers already within the first two minutes :)
Anyhow, it's great I'm finally getting insight on how people deal with "impossible counter-intuitive" equations.
Keep the answers coming! This is getting very interesting.
2007-09-24 19:16:22 · update #1
The trick is to use limits, in particular L'Hopital's Rule. His rule states that if your function at a certain point is 0/0, you can take the derivative of the top and bottom and try again.
x/x
d/dx(x/x)
1/1=1
So, as you can see, the limit of x/x at zero is 1. That is why there is no hole in the graph.
2007-09-24 19:19:04 · answer #1 · answered by Anonymous · 1⤊ 2⤋
Good question deserves a good answer. x/x for the case of x=0 is not the same as 1/1, since 1/1 will be 1, but 0/0 is defined as not be determinable, per se. We can apply limit tests to determine what really happens to a given function, and I believe in this case, it is continuous at 0.
2007-09-24 19:14:29 · answer #2 · answered by cattbarf 7 · 0⤊ 1⤋
x/x = 1 provided x <> 0. Division by 0 is just not defined, hence graphs with holes. y = (x²-4)/(x-2) looks just like y = x+2, but with a hole at x=2.
2007-09-24 19:15:17 · answer #3 · answered by Philo 7 · 0⤊ 1⤋
Whats the last step when you solve any function for x? Its to verify your solutions per the original equation! You could and should simplify to 1 in order to graph the function... it would make your arithmetic easy. But you still have to verify for all values... and x = 0 in the function x/x doesnt work
2007-09-24 19:14:03 · answer #4 · answered by Anonymous · 0⤊ 1⤋
Yes it can be undefined. If x = 0 the answer is undefined since division by zero is undifined.
2007-09-24 19:13:08 · answer #5 · answered by ? 5 · 0⤊ 1⤋
You are correct.
2007-09-24 19:11:20 · answer #6 · answered by Anonymous · 0⤊ 1⤋