I wanna know if x=0 can be the Asymptote or not ? please explain why ?! Thank you !
2006-12-23 17:49:28 · 5 answers · asked by A.B 1 in Science & Mathematics ➔ Mathematics
The place at which y=[(1/x)] and y=(1/x) is undefined is the same.
x=0 is the vertical asymptote because of division by zero
It doesn't change even if you take the floor of that because division is the first operation that you do before handling the function (floor(x)).
2006-12-23 17:54:02 · answer #1 · answered by ariotinlondon 2 · 0⤊ 0⤋
It is an asymptote.
An asymptote is a line that a function's graph approaches ever closer as the graph goes to the infinite region it is going to.
So x=0 is indeed a vertical asymptote for this function since getting closer to 0 from either side makes 1/x ever larger in magnitude and hence makes floor(1/x) also ever greater, causing x=0 to be ever closer approached by the graph of the given function.
2006-12-23 17:56:09 · answer #2 · answered by mulla sadra 3 · 0⤊ 0⤋
I assume when you say floor you mean the floor function of 1/x?
If so then x=0 is indeed the asymptote b/c 1/0 is undefined therefore an asymptote.
2006-12-23 17:54:29 · answer #3 · answered by Anonymous · 0⤊ 0⤋
The vertical asymptote is x = 0 because when x approaches to 0, y approaches to infinity.
Asymptote always relates to a limit.
2006-12-23 17:54:11 · answer #4 · answered by sahsjing 7 · 0⤊ 0⤋
it is the azsymtot with equation x=0
this is why
it is an asymptot because for every eps >0 there exist a delta > 0 such that |0 - floor(1/x) | < eps whenever |x| > delta
in fact tyou will have equality because of the floor function
2006-12-23 18:24:23 · answer #5 · answered by gjmb1960 7 · 0⤊ 0⤋