“asymptote”的概念、定义、翻译、参考文献-科学参考

asymptote

Physics

A line that a curve approaches but only touches at infinity.

Mathematics

A line l is an asymptote to a curve if the distance from a point P to the line l tends to zero as P tends to infinity along some unbounded part of the curve. Consider the following examples:

$(i) y = \frac{x + 3}{(x + 2) (x - 1)}, (ii) y = \frac{3 x^{2}}{x^{2} + x + 1}, (iii) y = \frac{x^{3}}{x^{2} + x + 1} .$

Example (i) has x =−2 and x =1 as vertical asymptotes and y = 0 as a horizontal asymptote. Example (ii) has no vertical asymptotes and y = 3 as a horizontal asymptote. To investigate example (iii), it can be rewritten as

$y = x - 1 + \frac{1}{x^{2} + x + 1} .$

Then it can be seen that y = x−1 is a slant (or oblique) asymptote, that is, an asymptote that is neither vertical nor horizontal.

Statistics

If part of a graph is unbounded and there is a fixed straight line l such that the distance from a point P on the graph to l tends to 0 as OP → ∞, where O is the origin, then l is an asymptote to the curve. Alternatively, it is the limiting position of the tangent to the graph at P, as OP → ∞. For example, the asymptotes of the graph of $asymptote$ are y=2x+3 and x=2.
Asymptote. The dotted lines are the asymptotes (vertical, x=2; oblique, y=2x+3) of the graph y=2x+3−.

Chemical Engineering

A straight line that is closely approached by a curve so that the perpendicular distance between them decreases to zero at an infinite distance from the origin.

单词	asymptote
释义	asymptote Physics A line that a curve approaches but only touches at infinity. Mathematics A line l is an asymptote to a curve if the distance from a point P to the line l tends to zero as P tends to infinity along some unbounded part of the curve. Consider the following examples: $(i) y = \frac{x + 3}{(x + 2) (x - 1)}, (ii) y = \frac{3 x^{2}}{x^{2} + x + 1}, (iii) y = \frac{x^{3}}{x^{2} + x + 1} .$ Example (i) has x =−2 and x =1 as vertical asymptotes and y = 0 as a horizontal asymptote. Example (ii) has no vertical asymptotes and y = 3 as a horizontal asymptote. To investigate example (iii), it can be rewritten as $y = x - 1 + \frac{1}{x^{2} + x + 1} .$ Then it can be seen that y = x−1 is a slant (or oblique) asymptote, that is, an asymptote that is neither vertical nor horizontal. Statistics If part of a graph is unbounded and there is a fixed straight line l such that the distance from a point P on the graph to l tends to 0 as OP → ∞, where O is the origin, then l is an asymptote to the curve. Alternatively, it is the limiting position of the tangent to the graph at P, as OP → ∞. For example, the asymptotes of the graph of $asymptote$ are y=2x+3 and x=2. Asymptote. The dotted lines are the asymptotes (vertical, x=2; oblique, y=2x+3) of the graph y=2x+3−. Chemical Engineering A straight line that is closely approached by a curve so that the perpendicular distance between them decreases to zero at an infinite distance from the origin.
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