- #1

- 12

- 0

## Homework Statement

Find the limit of:

^{(x^2+y^2+2xy)/(x^2+y^2)}

## Homework Equations

^{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?