Question

Need some help finding limit. I tried to show that the limit DNE by setting x as 0, but that didn't work, so I tried setting y as 0, that didn't work either, so I tried setting y as 2, and that didn't work either. I am a bit stuck :/

lim (2xy-2y)/(x^2+y^2-2x+1)
X,Y-> (1,0)

Answer 1

sorry, I meant to say, not to find the limit, but to show that it doesn't exist. help is appreciated :)

Answer 2

what do we need to prove in order to define a limit as DNE?

Answer 3

in 2 dimensions its pretty simple, we have a left and a right approach ... not many ways to try out

but in higher dimensions, the 'paths' to approach a point border on the infinite.

Answer 4

show that there is at least 2 paths that lead to different results.

Answer 5

if y=x-1, what is our limit?

Answer 6

Ah okay my problem is that no matter what I substitute to try to show that there are two different limits, I keep getting 0... but I didn't think of trying x-1. I will try that right now.

Answer 7

okay thank you! I think I got it.

Answer 8

good job :)