Question

Consider

lim (x, y)→(0, 0)

x² + y²

xy

(see figure).

(a) Determine (if possible) the limit along any line of the form

y = ax.

(Assume

a ≠ 0.

If an answer does not exist, enter DNE.)

(b) Does the limit exist? Explain.

Yes, the limit exists. The limit is the same regardless of which path is taken.No, the limit does not exist. Different paths result in different limits.    

Answer 1