# Curve where both x and y approach infinity

• B
• Pjpic
In summary, there are many curves with the property that x approaches infinity as y approaches infinity, including straight lines and curves with powers. The choice of curve may depend on additional properties or context.
Pjpic
What is the equation for a curve where x approaches infinity as y approaches infinity?

I don't think I understand you well, but what about: ##x = y##
?

PeroK and jedishrfu
Krylov said:
I don't think I understand you well, but what about: ##x = y##
?
Wouldn't that be a straight line instead of a curve?

Pjpic said:
Wouldn't that be a straight line instead of a curve?
To me a straight line is a particular kind of curve, but if you prefer something that really "curves", then you could do ##x = y^2##. However, I believe you were also able to find that out?

Maybe it helps when you explain a bit more about the background of your question. There are lots of planar curves with the property that ##x \to \infty## as ##y \to \infty##. Are you looking for a curve among them that has some additional properties?

Pjpic
Krylov said:
To me a straight line is a particular kind of curve, but if you prefer something that really "curves", then you could do ##x = y^2##. However, I believe you were also able to find that out?

Maybe it helps when you explain a bit more about the background of your question. There are lots of planar curves with the property that ##x \to \infty## as ##y \to \infty##. Are you looking for a curve among them that has some additional properties?
I think I get it. Powers make a curve.

A straight line is a mathematical curve as well. It is just an interesting special case.

##y=ln(x)## also works as does ##y=e^x##

## 1. What is a curve where both x and y approach infinity?

A curve where both x and y approach infinity is a type of mathematical function that has an asymptote where both the x and y coordinates increase without bound. This means that as the values of x and y get larger and larger, the curve approaches a vertical line and a horizontal line, respectively.

## 2. How is a curve where both x and y approach infinity different from other curves?

A curve where both x and y approach infinity is different from other curves because it has two asymptotes instead of just one. This allows the curve to approach infinity in both the x and y directions, whereas other curves may only have one direction of infinite growth.

## 3. What are some real-life examples of a curve where both x and y approach infinity?

One real-life example of a curve where both x and y approach infinity is the trajectory of a projectile launched at an angle. As the projectile travels further and further, both the horizontal distance (x) and the vertical height (y) increase without bound. Another example is the population growth of certain species, where both the time (x) and the number of individuals (y) continue to increase without limit.

## 4. How can a curve where both x and y approach infinity be represented mathematically?

A curve where both x and y approach infinity can be represented mathematically using a rational function, such as f(x) = x/y. This function has two asymptotes, one at x=0 and one at y=0, and as x and y get larger, the function approaches infinity in both directions.

## 5. Are there any practical applications for understanding curves where both x and y approach infinity?

Yes, there are practical applications for understanding curves where both x and y approach infinity. For example, in physics and engineering, these types of curves can help predict the behavior of projectiles or model growth patterns in populations. In economics, understanding these curves can aid in analyzing market trends and predicting future trends. Additionally, understanding these curves can also help in solving complex mathematical problems and equations.

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