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If x=a is a vertical asymptote of f(x), then x=a+h is a vertical asymptote of f(x-h) If y=c is a horizontal asymptote of f(x), then y=c+k is a horizontal asymptote of f(x)+k; If a known function has an asymptote, then the scaling of the function also have an asymptote. If y=ax+b is an asymptote of f(x), then y=cax+cb is an asymptote of cf(x)
Determine the asymptotes of the curve. Also determine from which side the curve approaches the asymptotes and where the asymptotes intersect the curve. [1] Equate first and second derivatives to 0 to find the stationary points and inflection points respectively.
The function f(n) is said to be "asymptotically equivalent to n 2, as n → ∞". This is often written symbolically as f ( n ) ~ n 2 , which is read as " f ( n ) is asymptotic to n 2 ". An example of an important asymptotic result is the prime number theorem .
The unit hyperbola is blue, its conjugate is green, and the asymptotes are red. In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation = In the study of indefinite orthogonal groups, the unit hyperbola forms the basis for an alternative radial length
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
The opening weeks of the NBA season have been besieged by absent stars. This past week’s games turned out to be particularly destructive. First, on Thursday, news broke that Philadelphia 76ers ...
The asymptotes of a truncus are found at x = -b (for the vertical asymptote) and y = c (for the horizontal asymptote). This function is more commonly known as a reciprocal squared function, particularly the basic example 1 / x 2 {\displaystyle 1/x^{2}} .
Image credits: Westford Animal Control / Facebook A woman walking by the Nabnasset Lake in Westfold, Massachusetts, noticed a cat stuck on the ice in the middle of the lake and immediately called ...