Evaluate the limit and explain why each student is correct/incorrect

Morgan, Avery, and Taylor are asked to evaluate the limit lim ry2 - 2x2 (x,y)=(8,4) 14 - 4x2 . Morgan writes lim y2 - 2.x2 (x,y) =(8,4) y4 - 4x2 and concludes from this that the limit does not exist. . Avery notes that along x = 0. my - 2.2 0 - 0 ry2 - 2.x2 0 -2.x2 y4 - 4x2 y4 - 0 = 0 and that along y = 0, 14 - 4x2 0 - 412 Avery concludes that the limit does not exist since the function tends to different values along different paths. . Taylor notes that along y = mu, xy2 - 2.x2 x(mx)2 - 2.x2 max - 2 (max)4 - 4x2 mix4 - 4' , x 0, and as a - 0, m'x - 2 m4x4 - 4 Taylor concludes that the limit exists and is equal to Determine which students, if any, provided a correct response. If a student did not provide a correct response, make sure to explain what error (or errors) they made. If none of the students are correct, calculate the limit correctly, or explain why it does not exist