Question

I have this function: f(x,y)=ln(x^2+y^2)
Find the boundary of the function's domain

Answer 1

i can only think of the restriction that ln cannot be 0
x^2 + y^2 = 0 would only occur at (0,0)

Answer 2

why? what makes (0,0) the boundary point?

Answer 3

can you explain?

Answer 4

I'm not particularly familiar with domain 'boundaries', but i do know that logarithms are not defined for zero, so the domain would not include (0,0) since
ln(0^2 + 0^2) = ln(0)

Answer 5

just what i'm thinking though, I'm hoping somebody can confirm. :P

Answer 6

yeah cause i still dont get it, cause apparently in my book it sats that a point(x,y) is a boundaary point of R if every disk centered at (x,y) contains the points tha lie outside of T as well as points that lie in R

Answer 7

I mean R not T

Answer 8

and i dont even understand that definition

Answer 9

yeah, that definition is outside of what I know of math...

Answer 10

i mean i am sure i would get it, if someone could help me understand this question.

Answer 11

I'm pretty sure I can answer it if I can figure out exactly what it is asking as well

Answer 12

that is exactly how the question is worded in my book

Answer 13

"a point(x,y) is a boundary point of R if every disk centered at (x,y) contains the points tha lie outside of R as well as points that lie in R"
is what you say your book says
that seems to fit the description of the point (0,0)
center a disk at (0,0) every point (x,y) in that disk is in R
but within that disk is also the point (0,0), which is not in R
so the point is (0,0) I believe

Answer 14

yes (0,0) is the answer, so your explination seems to make sense

Answer 15

for instance make a disk of radius r\[x^2+y^2=r^2\]r can be any size, and any point in it except (0,0) is in R
hence
"every disk centered at (x,y)=(0,0) contains the points that lied outside of R as well as points that lie in R"
as is commanded by your theorem

Answer 16

all that colored region is R
(0,0) is not included