0
Want this question answered?
Be notified when an answer is posted
Add your answer:
Earn +20 pts
How do you determine if a graph is asymptotic?
A graph of y against x has an asymptote if, its y value approaches some value k but never actually attains it. The value k is called its asymptotic value. These are often "infinities" when a denominator in the function approaches 0. For example, y = 1/(x-2) has an asymptotic value of minus infinity when x approaches 2 from below and an asymptotic value of + infinity from above. But the asymptotic value need not be infinite - they could be a "normal number. For example y = 3-x + 2.5 has an asymptotic value of 2.5. y is always greater than 2.5 and as x increases, it comes closer and closer to 2.5 but never actually attains that value.
Is it possible for a function that has a horizontal asymptote to attain the value of an asymptote?
Yes. Think of a function that starts at the origin, increases rapidly at first and then decays gradually to an asymptotic value of 0. It will have attained its asymptotic value at the start. For example, the Fisher F distribution, which is often used, in statistics, to test the significance of regression coefficients. Follow the link for more on the F distribution.
What about rational functions creates undefined and asymptotic behavior?
A rational function is the ratio of two polynomial functions. The function that is the denominator will have roots (or zeros) in the complex field and may have real roots. If it has real roots, then evaluating the rational function at such points will require division by zero. This is not defined. Since polynomials are continuous functions, their value will be close to zero near their roots. So, near a zero, the rational function will entail division by a very small quantity and this will result in the asymptotic behaviour.
In mathematics what is asymptotic analysis?
In mathematics, an asymptotic analysis is a method of describing limiting behaviour. The methodology has applications across science such as the analysis of algorithms.
The graph of the equation below is a hyperbola. What are the slopes of the hyperbola's asymptotic?
7/12 and 7/12 is the answer
How do you determine if a graph is asymptotic?
A graph of y against x has an asymptote if, its y value approaches some value k but never actually attains it. The value k is called its asymptotic value. These are often "infinities" when a denominator in the function approaches 0. For example, y = 1/(x-2) has an asymptotic value of minus infinity when x approaches 2 from below and an asymptotic value of + infinity from above. But the asymptotic value need not be infinite - they could be a "normal number. For example y = 3-x + 2.5 has an asymptotic value of 2.5. y is always greater than 2.5 and as x increases, it comes closer and closer to 2.5 but never actually attains that value.
Is it possible for a function that has a horizontal asymptote to attain the value of an asymptote?
Yes. Think of a function that starts at the origin, increases rapidly at first and then decays gradually to an asymptotic value of 0. It will have attained its asymptotic value at the start. For example, the Fisher F distribution, which is often used, in statistics, to test the significance of regression coefficients. Follow the link for more on the F distribution.
What about rational functions creates undefined and asymptotic behavior?
A rational function is the ratio of two polynomial functions. The function that is the denominator will have roots (or zeros) in the complex field and may have real roots. If it has real roots, then evaluating the rational function at such points will require division by zero. This is not defined. Since polynomials are continuous functions, their value will be close to zero near their roots. So, near a zero, the rational function will entail division by a very small quantity and this will result in the asymptotic behaviour.
What has the author Peter D Miller written?
Peter D. Miller has written: 'Applied asymptotic analysis' -- subject(s): Asymptotic theory, Differential equations, Integral equations, Approximation theory, Asymptotic expansions
What is conditional asymptotic notation?
30
What has the author Edward Thomas Copson written?
Edward Thomas Copson has written: 'Asymptotic expansions' -- subject(s): Asymptotic expansions
In mathematics what is asymptotic analysis?
In mathematics, an asymptotic analysis is a method of describing limiting behaviour. The methodology has applications across science such as the analysis of algorithms.
Can lines of curvature be asymptotic curves?
A curve may be both asymptotic and a line of curvature, in which case the curve is a line (such as the rulings of a ruled surface).
Define worst-case of an algorithm?
Asymptotic
What has the author Musafumi Akahira written?
Musafumi Akahira has written: 'The structure of asymptotic deficiency of estimators' -- subject(s): Asymptotic efficiencies (Statistics), Estimation theory
Can the graph of a function have a point on a vertical asymptote?
No. The fact that it is an asymptote implies that the value is never attained. The graph can me made to go as close as you like to the asymptote but it can ever ever take the asymptotic value.
What has the author J Lewowicz written?
J. Lewowicz has written: 'Asymptotic directions of the solutions of linear differential equations' -- subject(s): Asymptotic theory, Linear Differential equations
