Physical Asymptote Homework: Trajectory y=x^4-x^2 & Limit y(x)=h

In summary, the problem is to plot a two-dimensional trajectory parametrized by y = x^4 - x^2 under the constraint ymax = h. This gives a natural constraint on x as well, depending on the value of h. The plot will vary based on the chosen value of h.
  • #1
LagrangeEuler
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Homework Statement


For example particle performs a motion in x-y plane. In y there are walls from both side so particle can go in y direction from zero to [tex]h[/tex]. I need to plot trajectory. If I got trajectory [tex]y=x^4-x^2[/tex] then
[tex]\lim_{x\to \infty}y(x)=\infty[/B]

Homework Equations

The Attempt at a Solution


If I got trajectory [tex]y=x^4-x^2[/tex] then
[tex]\lim_{x\to \infty}y(x)=\infty[/tex], but because of the condition I may say that [tex]\lim_{x\to \infty}y(x)=h[/tex]. Maybe then [tex]y=h[/tex] is some natural horisontal asymptote?[/B]
 
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  • #2
Hi. It's hard to understand what your problem exactly is. Could you clarify it maybe by giving its original statement?
If you are asked to plot a two-dimensional trajectory parametrized by:
y = x4–x2,
Under the constraint: ymax= h,
Then it gives you a natural constraint on x as well, as a function of h; if you need to plot this you'll have to assign an arbitrary value to h so that you can plot something.
Now depending on this value, your plot will not always look the same but that's all you can do with the given information...
 

1. What is a physical asymptote?

A physical asymptote is a line or curve that a graph approaches but never touches. It represents the behavior of a function as the input approaches a certain value.

2. How is a physical asymptote different from a vertical asymptote?

A physical asymptote is a curve that the graph approaches but never touches, while a vertical asymptote is a line that the graph gets infinitely close to but never crosses.

3. How do you find the physical asymptote for a given function?

To find the physical asymptote for a given function, you can use the limit of the function as the input approaches a certain value. If the limit is a finite number, then there is a physical asymptote at that value. If the limit is infinity, then there is no physical asymptote.

4. Can a function have multiple physical asymptotes?

Yes, a function can have multiple physical asymptotes. This can happen if the limit of the function approaches different values as the input approaches different values.

5. How does the function y=x^4-x^2 behave near its physical asymptote?

As the input approaches the physical asymptote, the function will approach the value of the limit at that point. In this case, the function will approach the value of h as x approaches infinity or negative infinity.

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