I have posted the problem 2.12 from Spivaks calculus on Manifolds below along with a solution for it. Before looking at this solution, I attempted to prove it by writing this
$\lim_{(h,k)\to 0} \dfrac{|f(h,k)|}{|(h,k)|} \leq \lim_{(h,k)\to 0} \dfrac{M|(h,k)|^2}{|(h,k)|}$ for some $M>0$
because earlier there was a question asking
And to continue the proof we can now write
$\lim_{(h,k)\to 0} M|(h,k)| = 0$
Does this proof work?
And here is he problem along with the solution
Thanks
Solution
