Use polar coordinates to find the limit

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To find the limit using polar coordinates, one must convert the Cartesian coordinates (x, y) to polar coordinates (r, θ), where r approaches 0 as (x, y) approaches (0, 0). The discussion highlights the importance of understanding the behavior of continuous functions as r approaches 0. Participants are encouraged to clarify the steps taken and seek guidance on determining the limit. The conversation emphasizes the need for a solid grasp of limits in the context of polar coordinates. Ultimately, the goal is to accurately evaluate the limit as the point approaches the origin.
Faka
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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)]
 

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What steps have you made so far?
 
I've done this so far. I do not know how to determine what the limit is.
 

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Looks like a continuous function of r to be, what are the limits of continuous functions?
 
what do you mean exactly?
 
I hope this is right :smile:
 

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