# Thread: Domain of a multivariable function

1. ## Domain of a multivariable function

Given $\displaystyle f(x,y)=\frac{6x^2+13xy+5y^2}{2x+y}$

a) Find the domain of f.
b) How can it be defined at all points not in its domain so the resulting
function is continuous everywhere in the xy-plane?

a) its domain is the whole xy plane expept for the line y=-2x.

b) I really have no clue how to approach this. Can somebody help??

2. It is easy to verify that...

$\displaystyle \frac{6x^{2} + 13 xy + 5 y^{2}}{2x+y}= \frac{6x^{2} + 3xy}{2x+y} + \frac{10xy + 5y^{2}}{2x+y} = 3x + 5y$

... so that $\displaystyle f(*,*)$ has as domain the whole x-y plane and it is continous everywhere...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. Ah thank you!!

4. Do you attend McGill University Makarooney? This problem it looka very familiar indeed...

5. Originally Posted by Neville S.
Do you attend McGill University Makarooney? This problem it looka very familiar indeed...

Lol yes. This is one of the assignment questions for Intermediate calculus eng. You must be in one of those sections then...

6. or... the prof.... O_o

7. you sir are in BIG trouble! lol no i am also in inter cal at mcgill, ive been googling and i figured you were from my class. keep asking the questions, cuz you're helping a lot of people! (You're the first hit on google!)