Curve where both x and y approach infinity

Click For Summary
SUMMARY

The discussion centers on identifying equations for curves where both x and y approach infinity. Participants confirm that while the equation x = y represents a straight line, it is indeed a specific type of curve. Alternatives such as x = y^2, y = ln(x), and y = e^x are proposed as examples of curves that meet the criteria of both variables approaching infinity. The conversation emphasizes the distinction between straight lines and more complex curves in mathematical analysis.

PREREQUISITES
  • Understanding of basic algebraic equations
  • Familiarity with the concept of limits in calculus
  • Knowledge of different types of curves in mathematics
  • Basic understanding of exponential and logarithmic functions
NEXT STEPS
  • Research the properties of polynomial curves, specifically quadratic functions
  • Explore the behavior of exponential functions as they approach infinity
  • Study the applications of logarithmic functions in mathematical modeling
  • Investigate the concept of asymptotic behavior in calculus
USEFUL FOR

Mathematicians, students studying calculus, and anyone interested in the properties of curves and their equations in mathematical analysis.

Pjpic
Messages
235
Reaction score
1
What is the equation for a curve where x approaches infinity as y approaches infinity?
 
Physics news on Phys.org
I don't think I understand you well, but what about: ##x = y##
?
 
  • Like
Likes   Reactions: 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?
 
  • Like
Likes   Reactions: 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##
 

Similar threads

Undergrad Questions about algebraic curves and homogeneous polynomial equations
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Notion of congruent curve along a vector field
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How to find inverse coordinates?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
  • · Replies 2 ·
Replies
2
Views
2K
High School Solving for integral curves- how to account for changing charts?
  • · Replies 4 ·
Replies
4
Views
2K
High School Rabbit and Turtle Race: A Mathematical Analysis of Infinity and Probability
  • · Replies 17 ·
Replies
17
Views
4K
High School Axes on a hyperbolic plane
  • · Replies 4 ·
Replies
4
Views
2K
High School East-West error at regular points on the Azimuthal Equidistant Map
  • · Replies 3 ·
Replies
3
Views
3K
High School Math Equation for Backward Going Curve?
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Question about two interference patterns viewed at infinity
  • · Replies 7 ·
Replies
7
Views
2K