Why can horizontal asymptotes be crossed? - Physics Forums
2007年8月5日 · A function can cross its vertical asymptote, though not more than once and certainly not infinitely many times like it can its horizontal asymptote. For example, f(x) := 1/x for x !=0 and f(0) := 0. I don't think I would exactly call that crossing.
Why is y=a a horizontal asymptote on the polar coordinates?
2010年6月8日 · A vertical asymptote occurs when the curve approaches a vertical line, such as r = ±a. A horizontal asymptote occurs when the curve approaches a horizontal line, such as r = 0. These types of asymptotes have specific equations and can have different effects on the behavior of …
Determining the horizontal asymptote - Physics Forums
2024年4月9日 · My interest is on the horizontal asymptote, now considering the degree of polynomial and leading coefficients, i have ##y=\dfrac{2}{1} =2## Therefore ##y=2## is the horizontal asymptote. The part that i do not seem to get is (i already checked this on desmos) why an asymptote can be regarded as such if it is crossing the curve. In my small ...
What is an asymptote and why doesn't parabola have one?
2007年10月1日 · But they *still* don't increase quickly enough to have an asymptote. The simplest example of a function that does have an asymptote is 1/x . this function increases even more quickly than any function of the form n^x or n^n^x or n^n^n^x etc. Every function that increases more quickly than 1/x does have at least one asymptote. 1/x^2, 1/x^100 etc
Describing behavior on each side of a vertical asymptote - Physics …
2006年1月2日 · The behavior on each side of a vertical asymptote can be described using limit notation. For example, if the asymptote is located at x=a, the limit of the function as x approaches a from the left side would be written as lim x→a- f(x) and the limit from the right side would be written as lim x→a+ f(x).
How to find oblique asymptotes for any function in general?
2005年7月11日 · To find the oblique asymptote, you must use polynomial long division, and then analyze the function as it approaches infinity. Taking the limit first, like HallsofIvy did, is wrong because 11/x and 1/x approach infinity at different rates, and therefore add to the numerator and denominator in slightly different ways.
Horizontal asymptotes - approaches from above or below?
2009年2月22日 · I seem to be having a lot of difficulty finding whether for a horizontal asymptote, whether the curve approaches the asymptote from above or below. For example, for the problem y = \\frac{6x + 1}{1 - 2x}, I know that: For the vertical asymptote, x = 1/2, and that \\lim_{x \\to...
Asymptote of a curve in polar coordinates - Physics Forums
2017年4月14日 · FAQ: Asymptote of a curve in polar coordinates What is the definition of an asymptote in polar coordinates? In polar coordinates, an asymptote is a straight line that the curve approaches but never touches, as the distance between the curve and the line approaches zero as the distance from the origin increases.
Is x+y = -1 an oblique asymptote for the folium of Descartes curve?
2010年10月24日 · In summary, the curve x^3+y^3=3xy is called the folium of Descartes. By rewriting the equation and using the definition of an oblique asymptote, we can show that x+y = -1 is an oblique asymptote for the curve. This means that as x approaches infinity, the difference between the curve and the asymptote approaches 0, making it an oblique asymptote.
Oblique Asymptotes: What happens to the Remainder? - Physics …
2011年10月24日 · When finding an oblique asymptote, the remainder becomes 0, indicating that the function is getting closer and closer to the asymptote. Can a function have more than one oblique asymptote? Yes, a function can have multiple oblique asymptotes depending on the behavior of the function at infinity.