# Multivariable Limits

## Homework Statement

Find the limit of:
(x^2+y^2+2xy)/(x^2+y^2)

x = r*cos(theta)
y= r*sin(theta)

## The Attempt at a Solution

So what I did was change to polar coordinates. Then it simplifies to:

(r^2 + 2r^2cos(theta)sin(theta) )/r^2

Factoring out an r^2 from everything you get:
1 + 2cos(theta)sin(theta)

And the limit as r and theta go to zero would appear to be 1. However if I plug in numbers very close to zero on my calculator it tells me that the limit is 2. Little help?

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Dick
Homework Helper
Your limit depends on theta. That means the limit is different as you approach (0,0) in different ways. E.g. if you approach along the x axis, x=t, y=0 (theta=0), you get 1. If you approach along a line x=t, y=t, (theta=pi/4) you get 2. What does this tell you about the existence of the limit?

It doesnt exist? So when i do that method if I find i have thetas in my answer then the limit does not exist?

Dick