Find the limit, if it exists. Step 1 xy lim (x, y) (0, 0) x + y To examine xy lim (x,y) (0, 0) x + On this path, all points have y = 0 xy lim (x, y) (0, 0) x + y Step 2 Since y = 0 for all points on this path, then we have When x is positive, we have xy lim (x, y) (0, 0) x + y first approach (0, 0) along the x-axis. When x is negative, we have xy lim (x, y) (0, 0) x + y = lim X 0 Step 3 Similarly, approaching along the y-axis yields a limit equal to 0. Since these two limits are the same, we will examine another approach path. Approach (0, 0) along the curve y = x. = lim 0 + X X. 0 X y = 0 = lim x x 0 3 3 x + 0 x + x4 x + x4 lim x 0 lim X 0- 0 x + x x x+x X X