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## Homework Statement

Hey guys. I am having a little trouble answering this question. I am teaching myself calc 3 and am a little confused here (and thus cant ask a teacher). I need to find the limit as (x,y) approaches (0,1) of f(x,y) when f(x,y)=(xy-x)/(x^2+y^2-2y+1).

## Homework Equations

|f(x,y)-L|<epsilon

0<sqrt((x-a)^2+(y-b)^2))<delta

I made L=0, assumed epsilon>0

## The Attempt at a Solution

Looking at the answer I see that the limit does not exist; however when I do the epsilon delta proof I cant see where I went wrong because I keep getting the result that it does :( ? So I attached a picture detailing my argument and I would love for someone to tell me where I went wrong. I chose L in the epsilon delta definition to be 0 because this is what I get when I approach (0,1) along x=0, y=1, and y=x^3+1 . I am aware that the limit does not exist because if you travel along x=y^2-1 you get a value other than zero. However my only concern is why my logic is not correct in the attached image. Thanks a lot! Also if you have tips for doing these epsilon delta proofs I would love to hear them.

#### Attachments

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