1. The problem statement, all variables and given/known data Find the limit, if it exists, or show that the limit does not exist. limit (x,y) --> (0,0) a) f(x,y) = (xycosy) / (3x^2 + y^2) b) f(x,y) = (xy) / sqrt(x^2 + y^2) c) f(x,y) = ((x^2)ye^y) / ((x^4) + 4y^2) 2. Relevant equations 3. The attempt at a solution a) For this one, I did (0,y)-->(0,0) and got 0; then did (x,0) --> (0,0) and got 0. Then I substituted y=x, so (x,x) --> (0,0). I ended up getting ((x^2)cosx) / 4x^2; which I evaluated as x goes to zero, the limit would not exist (since the bottom would be zero). b) Again I did x=0, and y=0 and came up with 0 for both of those. Would I then, substituted y=x again? Ending up with x^2 / xsqrt(2), so x/sqrt(2) goes to zero as x goes to zero. So the limit would be zero. Would I have to try more paths? c) Again, x=0, y=0 resulted in limit of 0. Next I attempted x = sqrt(y); so ((y^2)e^y) / ((y^2) + 4y^2) which lead to (1/5)e^y. So as y goes to zero, e^y goes to 1, and the limit goes to 1/5. Therefore, the limit does not exist. Did I go about these in the right way, and would I need to test more paths for each of them?