Use polar coordinates to find the limit

In summary, polar coordinates are a way of representing points in a two-dimensional plane using a distance from the origin and an angle from a reference line. To find the limit using polar coordinates, you first convert the function into polar form and then approach the limit point by setting the distance from the origin to be the limit value and letting the angle approach 0. The advantages of using polar coordinates for finding limits include simplifying complex functions, visualizing function behavior, and identifying symmetries and patterns. However, limitations of using polar coordinates for finding limits include not working for all types of functions and the time-consuming conversion process for more complex functions. Additionally, polar coordinates can be extended to higher dimensions, such as finding limits in three-dimensional space.
  • #1
Faka
25
0
Hi!
Is there somebody, who can help me with this exercise:
"Use polar coordinates to find the limit. [If (r, θ ) are polar coordinates of the point (x,y) with r ≥ 0, note that r --> 0+ as (x,y) --> (0,0)]
 

Attachments

  • Limit.jpg
    Limit.jpg
    2.6 KB · Views: 499
Physics news on Phys.org
  • #2
What steps have you made so far?
 
  • #3
I've done this so far. I do not know how to determine what the limit is.
 

Attachments

  • Limit 2.jpg
    Limit 2.jpg
    7.2 KB · Views: 909
  • #4
Looks like a continuous function of r to be, what are the limits of continuous functions?
 
  • #5
what do you mean exactly?
 
  • #6
I hope this is right :smile:
 

Attachments

  • Limit 3.jpg
    Limit 3.jpg
    8.6 KB · Views: 1,185

1. What are polar coordinates?

Polar coordinates are a way of representing points in a two-dimensional plane using a distance from the origin and an angle from a reference line.

2. How do you find the limit using polar coordinates?

To find the limit using polar coordinates, you first convert the function into polar form. Then, you approach the limit point by setting the distance from the origin to be the limit value and letting the angle approach 0.

3. What are the advantages of using polar coordinates to find the limit?

One advantage of using polar coordinates is that it can simplify complex functions and make it easier to visualize the behavior of the function near a limit point. It can also help identify symmetries and patterns in the function.

4. Are there any limitations to using polar coordinates for finding limits?

One limitation of using polar coordinates is that it may not work for all types of functions, such as functions with vertical asymptotes or functions with multiple limit points. Additionally, the conversion from rectangular to polar form can be time-consuming for more complex functions.

5. Can polar coordinates be used to find limits in higher dimensions?

Yes, polar coordinates can be extended to higher dimensions, such as finding limits in three-dimensional space. In this case, the distance from the origin is represented by a radius, and the angle is replaced by a set of angles or spherical coordinates.

Similar threads

Show proof of point C in the given problem that involves Polar equation
    • Calculus and Beyond Homework Help
Replies
3
Views
87
Integration of acceleration in polar coordinates
    • Calculus and Beyond Homework Help
Replies
24
Views
1K
Change of Variables: Integrals w/Polar Coordinates
    • Calculus and Beyond Homework Help
Replies
2
Views
847
Calculate this Integral around the Circular Path using Green's Theorem
    • Calculus and Beyond Homework Help
Replies
3
Views
236
Graphing Polar Coordinates: 0 ≤ θ ≤ π and 0 ≤ r ≤ 4
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Trying to find this double integral using polar coordinates
    • Calculus and Beyond Homework Help
Replies
14
Views
2K
Triple Integral of y^2z^2 over a Paraboloid: Polar Coordinates Method
    • Calculus and Beyond Homework Help
Replies
6
Views
1K
Problem figuring out the surface of integration
    • Calculus and Beyond Homework Help
Replies
2
Views
798
Polar coordinates of the centroid of a uniform sector
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Trying to use polar coordinates to find the distance between two points
    • Calculus and Beyond Homework Help
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top