Let $f:\mathbb{R^3} \rightarrow \mathbb{R}$ be defined by $f(x,y,z)=xy+yz+xz$. Show using the definition of differentiability that f is differentiable at the point a=(1,1,1).
Is it true that if $f$ is differentiable at a, then $\\lim_{x\to(1,1,1)} \frac{||f(x)-f(a)-J(x-a)||}{||x-a||}=0$ (where J is the jacobian of f at a)? Would you use this to prove the question above?
Yes, and it is just what you are required to do.