Hi,
The question asks to check if this funcion: sin( x^2 + y^2 ) / x^2 + y^2 is continuous or not which I already found out since its domain is {(x,y): x!=0 and y!=0}
But now its asks to check whether it can be redefined to be continous or not about which I am very confused. So here's what I think:
The function will become one when z tends to zero whihc makes the function continuous at zero and I think everywhere. But I don't have the clear understanding of this thing.
Kindly clear my understanding about it up since I am having a limited knowldge in this area and let me know if what I think is correct or not.
Thank you so much!
Polar coordinates are used for many purposes! But, specifically, if you have a two dimensional problem and are taking the limit at (0, 0), then polar coordinates have the advantage that the distance from a point to (0, 0) is measured by the single variable r. If taking the limit as r goes to 0 gives a value that does NOT depend on , then that value is the limit as we approach (0, 0) from any direction. If the result does depend on , then the limit does not exist.