Question

limit (x^2+y^2)/(x+y)^2 as (x,y)->(0,0)

I don't know how to prove it doesn't exist. Please help!

Answer 1

Consider the line through the points (3,2,5) and (1,1,1). Consider the plane A that is perpendicular to this line, and passing through the point (-1,0,2). Consider the plane B that passes through the points (1,-1,0), (0,2,0), and (0,5,2). Consider the intersection of plane A and plane B. Write the equation of the line of intersection.

Answer 2

type your equation onto the website wolfram alpha ... google the website if you're unfamiliar with it.

Answer 3

along x=y, the expression is

2x^2/4x^2 = 1/2

along x=2y, we have

5y^2/9y^2 = 5/9

In other words, as we approach (0,0) along different paths, the limit varies, so cannot be said to exist as a single number.