“3. One of the following functions has a limit at (0,0) element of R^2, the other does not. Decide which one has the limit, the value of the limit, and justify your answers for each function.”

3b) Since it is given that either L_a or L_b exists, and L_a DNE, then L_b exists. And since if the limit exists it must be 0, ergo L_b = 0 QED.

Another opportunity for regrets; why must humor always accompany ignorance?