ONUS: Limit Computation: Evaluating xy/(x^2+y^2) at Origin

In summary, the conversation is about finding the limit of xy/(x^2+y^2) when (x,y) approaches (0,0) along different curves. The person asking for help has already solved the problem using polar coordinates and apologizes for any confusion.
  • #1
brad sue
281
0
Hi ,
I have difficulty to find the folowing questions about limit computation.
IF lim xy/(x^2+y^2) ( when (x,y)---(0,0))
Evaluate the limit as (x,y) approaches the origin along:
a) The spiral r=0, θ >0
b) The differentiable curve y=f(x), with f(0)=0
c) The arc r=sin(θ )
Thank you
B
 
Physics news on Phys.org
  • #2
brad sue said:
Hi ,
I have difficulty to find the folowing questions about limit computation.
IF lim xy/(x^2+y^2) ( when (x,y)---(0,0))
Evaluate the limit as (x,y) approaches the origin along:
a) The spiral r=0, θ >0
b) The differentiable curve y=f(x), with f(0)=0
c) The arc r=sin(θ )
Thank you
B

ANy help please?
 
  • #3
Have you tried converting your expression to polar?
 
  • #4
Have you yet done any work on the problem? There should be at least one thing you can do that is very clear...
 
  • #5
Hurkyl said:
Have you yet done any work on the problem? There should be at least one thing you can do that is very clear...

Sorry I found out with the polar coordinates.I am ok now Sorry about everything.

B
 

FAQ: ONUS: Limit Computation: Evaluating xy/(x^2+y^2) at Origin

What is the purpose of the ONUS limit computation?

The ONUS limit computation is used to evaluate the value of an expression, xy/(x^2+y^2), at the origin (0,0). This can help determine the behavior of the expression as x and y approach 0, and can be useful in solving various mathematical problems.

How is the ONUS limit computation calculated?

The ONUS limit computation involves plugging in the values of x and y as they approach 0 into the expression xy/(x^2+y^2). This can be done by substituting 0 for both x and y, or by using various algebraic techniques to simplify the expression before plugging in the values.

What does the ONUS limit computation tell us about the behavior of the expression at the origin?

The ONUS limit computation can tell us whether the expression approaches a finite value, approaches infinity, or does not exist at the origin. This information is helpful in understanding the overall behavior of the expression and can be used to solve more complex mathematical problems.

Are there any limitations to the ONUS limit computation?

Yes, the ONUS limit computation may not always provide an accurate representation of the behavior of the expression at the origin. It is important to also consider the behavior of the expression as x and y approach 0 from different directions, and to use other mathematical tools such as graphing or calculus to fully understand the behavior of the expression.

What are some real-life applications of the ONUS limit computation?

The ONUS limit computation can be used in various fields such as physics, engineering, and finance. For example, in physics, it can be used to determine the limit of a function as a variable approaches 0, which can be useful in understanding the behavior of physical systems. In finance, it can be used to analyze the risk associated with certain investments by evaluating their limits as certain variables approach 0.

Similar threads

Prove if ##x<0## and ##y<z## then ##xy>xz## (Rudin)
Replies
2
Views
1K
Find f(x,y) given partial derivative and initial condition
Replies
6
Views
1K
Spivak, Ch 5 Limits, Problems 10c: Proving limit relationship
Replies
5
Views
1K
Volume integral of x^2 + (y-2)^2 +z^2 = 4 where x , y , z > 0
Replies
21
Views
2K
Limit of a two-variable function
Replies
5
Views
1K
Evaluate ##lim_{(x,y)\to(0,0)\frac{xy}{y-x^3}}##
Replies
3
Views
2K
Limit when x^2 + y^2 -> inf, am I solving it correctly?
Replies
8
Views
1K
Evaluating the limit of a multivariable function with paths?
Replies
8
Views
2K
Determine whether ## S[y] ## has a maximum or a minimum
Replies
18
Views
2K
Proving Irregularity of {(x, y, z) within R^3 : x^2 + y^2 - z^2 = 0}
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top