Oct 1, 2007 · 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

Aug 5, 2007 · 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.

Jun 8, 2010 · Since y=rsint, substituting r=y/sint into rt=a we get y=asint/t. By taking the limit of both sides as t->0 we get y=a. The thing I don't understand is, why is y=a a horizontal asymptote on the polar coordinates? Isn't y=a only an asymptote on the cartesian coordinates of the curve rt=a(when you convert it in terms of x and y)?

Apr 14, 2017 · I understood the concept behind how this asymptote is calculated, but I am not very fluent in mathematics to convert the above information into a comprehensive proof. Moreover, there is another statement that states that I have to make use of the information ## \lim_{\theta \rightarrow 0}x=+\infty##.

Feb 22, 2009 · 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...

Apr 9, 2024 · 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.

Oct 24, 2011 · An "asymptote" is a line that a curve approaches as x goes to, in this case, negative infinity and infinity. Yes, long division gives a quotient of -3x- 3 with a remaider of -1. Yes, long division gives a quotient of -3x- 3 with a remaider of -1.

Jan 2, 2006 · Find the vertical asymptotes of the graph of F(x) = (3 - x) / (x^2 - 16) ok if i factor the denominator.. i find the vertical asymptotes to be x = 4, x = -4. The 2nd part of the problem asks: Describe the behavior of f(x) to the left and right of each vertical asymptote.. I'm not sure...

Nov 30, 2007 · I was wondering if we include asymptotes as criticals: For example in y = x sqrt(4-x^2) when u find the critical points it gives u root 2 and negative root 2 But when I draw the graph I am missing the 2 and -2 which were the asymptotes …

May 22, 2011 · Homework Statement True False If the line x=1 is a vertical asymptote of y = f(x), then f is not defined at 1.Homework Equations none The Attempt at a Solution I originally believed this was true, but on finding it was false it sought a counter example: if for example f(x) = …