# So how do i do these limits?

• May 12th 2012, 05:12 AM
Brennox
So how do i do these limits?
1) Determine:

lim
(x,y)-->(-1,1)__________(x^2 - y^2)/(xy + y^2 + x + y)

2) Show that it doesnt exist.

lim
(x,y)--> (0,0)____________(2xy)/(x^2 + 2y^2)

If you plug in the numbers for (1) you get 0/0 same with (2), which doesnt seem right at all. Im pretty sure there is suppose to be atleast a few lines of working.
• May 12th 2012, 05:53 AM
Plato
Re: So how do i do these limits?
Quote:

Originally Posted by Brennox
1) Determine:
lim
(x,y)-->(-1,1)__________(x^2 - y^2)/(xy + y^2 + x + y)

2) Show that it doesnt exist.
lim
(x,y)--> (0,0)____________(2xy)/(x^2 + 2y^2).

For the first one note that \$\displaystyle x^2-y^2=(x+y)(x-y)\$ and \$\displaystyle xy+y^2+x+y=(x+y)(y+1)\$.
There is a common factor.
• May 12th 2012, 06:39 AM
Deveno
Re: So how do i do these limits?
for number (2), if we approach (0,0) along the line x = y, we get a limit of 2/3. if we approach (0,0) along the x-axis, we get a limit of 0. thus the limit cannot exist (any disk centered at (0,0) contains pieces of both lines).