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