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Here's something taken from www.freemathhelp.com: "A horizontal asymptote is a y-value on a graph which a function approaches but does not actually reach. Here is a simple graphical example where the graphed function approaches, but never quite reaches, y=0." The example never said anything about one part of the graph approaching it, but ...
1. The definition I'm familiar to, regarding real valued function f: R → R is the following. We say that y = l, where l ∈ R, is an horizontal asymptote for f(x) if lim x → + ∞f(x) = l. Analogous formulation for − ∞. As you can see this represent the first one of your condition, but the second isn't necessary. Here's graph of the ...
$\begingroup$ @peterwhy I thought the definition of a horizontal asymptote at y = a is that limit as x approaching positive or negative infinity, a is never met... When I graph this, I'm quite not sure where I'd have to actually look at to see to make sure that y=3 is the horizontal asymptote... $\endgroup$ –
This is a lot simpler of a problem than others posted here, but I was bored in class and decided to work out why a horizontal asymptote exists. Bear in mind that I am still fairly low on the “math ...
Finding the horizontal asymptote of a rational function ... By definition, an asymptote is approached by ...
Find all horizontal asymptote(s) of the function $\displaystyle f(x) = \frac{x^2-x}{x^2-6x+5}$ and justify the answer by computing all necessary limits. Also, find all vertical asymptotes and justify your answer by computing both (left/right) limits for each asymptote. MY ANSWER so far..
Horizontal asymptote definition. 2. Does $\frac{\sin x}{x}$ have a horizontal asymptote? Hot Network ...
In Stewart's Calculus book, there is an example of finding the horizontal asymptotes for f(x) = √2x2 + 1 3x − 5. And author starts solving it by writing that √x2 = x for positive x, so we can write numerator as √2x2 + 1 √x2. And the same he does for negative x. He says that √x2 = | x | = − x.
Rule 2) If the numerator and denominator have equal degrees, then the horizontal asymptote will be a ratio of their leading coefficients. Rule 3) If the degree of the numerator is exactly one more than the degree of the denominator, then the oblique asymptote is found by dividing the numerator by the denominator.
It seems (see 1, 2) that the formal definition of a horizontal asymptote is that the function simply needs to get "arbitrarily close" to the asymptote.