For each of the following prompts, provide an example of a function of two variables with the desired properties (with justification), or explain why sucha function does not exist.

a. A function p that is defined at (0,0), but lim)-(0,0) P(x, y) does not exist. b. A function q that does not have a limit at (0,0), but that has the same limiting value along any line y = ma as a 0. c. A function r that is continuous at (0,0), but lim)-(0,0) "(x, y) does not exist. d. A function s such that lim s(x, x) = 3 and (1,2)(0,0) lim (x,2z)-(0,0) s(x, 2x) = 6, %3D for which lim(zy)+(0,0) 8(x, y) exists. e. A function t that is not defined at (1, 1) but lim(a)(1,1) t(x, y) does exist.