Asked by Liz
Does the limit of xy/(x^2 + y^2) exist as (x,y)--->(0,0)?
Why or why not??
Why or why not??
Answers
Answered by
Steve
Since xy/(x^2+y^2) > 0 when xy > 0 and is <0 when xy < 0, if the limit is not zero, it does not exist.
As you approach (0,0) along the path x=y, the limit is 1/2
If you approach along y = -x, the limit is -1/2
Looks like there is no limit, since it depends on the approach path.
As you approach (0,0) along the path x=y, the limit is 1/2
If you approach along y = -x, the limit is -1/2
Looks like there is no limit, since it depends on the approach path.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.