Behavior at zero and at infinity

In summary, the conversation discusses a second order differential equation with singularities at zero and infinity. The individual is looking for help in finding the approximate behavior at these points. They receive suggestions to simplify the equation and change variables, ultimately leading to a solution.
  • #1
intervoxel
195
1
Hi,

I have a second order DE involving the first derivative and with singularities at zero and at infinity. I need the approximate behavior at zero and at infinity. I have the answer but I would like to know how to get there.

I don't know how to start this search. Any help?
 
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  • #2
For the singularity near x = 0 I would try keeping only the largest terms as x -> 0 and solve the simplified equation.

For the singularity near x = infinity, I would try to change variables to u = 1/x, and then do the same thing around u = 0.
 
  • #3
Bingo! Thanks a lot.
 

1. What is behavior at zero and at infinity?

Behavior at zero and at infinity refer to the behavior of a function or equation as the input variable approaches zero or infinity, respectively. It is important to understand this behavior in order to fully comprehend the behavior of a function as a whole.

2. How can I determine the behavior at zero and at infinity?

The behavior at zero and at infinity can be determined by analyzing the end behavior of a function. This means looking at the values of the function as the input variable approaches zero or infinity. It can also be determined by finding the limit of the function as the input variable approaches zero or infinity.

3. What is the difference between behavior at zero and at infinity?

The main difference between behavior at zero and at infinity is the direction of the input variable. At zero, the input variable is approaching from the left side of the number line, while at infinity, the input variable is approaching from the right side of the number line.

4. Why is it important to understand behavior at zero and at infinity?

Understanding behavior at zero and at infinity allows us to make predictions about the behavior of a function as a whole. It also helps us to identify any asymptotes or discontinuities in the function, which can affect its overall behavior.

5. How can behavior at zero and at infinity be applied in real life?

Behavior at zero and at infinity can be applied in various fields such as economics, physics, and engineering. For example, in economics, understanding the behavior of a demand curve at zero and at infinity can help businesses make decisions about their pricing strategies. In physics, the behavior of a particle at zero and at infinity can provide valuable insights into its motion and energy. In engineering, the behavior of a system at zero and at infinity can help engineers design and optimize their systems for maximum efficiency.

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