First question: Im trying to show the fundamental thm for gradients here with this function: T = x^2 + 4xy + 2yz^3 . a = (0,0,0) , b = (1,1,1) . For one path it works out as expected to 7. However when i use the path (0,0,0)->(0,0,1)->(0,1,1)->(1,1,1) , I end up with a value of 1 (0 for first step, 0 for second step and 1 for third step). There's also a path I have to check where z=x^2, y=x^2, dont know how to do this; Do i let dz = dxdx ? How do I deal with this? I havent covered these in calculus yet, just in my E-M text. Would like to know so I can complete my assignment, Thanks.