In 18.02 Problem set 4, Part II, Qn.4, can anyone please explain how the boundary test is done. Why is the boundary considered as x2+y2 = 27 and not x2+y2+z2 = 27 ?
Thanks.

Question

In 18.02 Problem set 4, Part II, Qn.4, can anyone please explain how the boundary test is done. Why is the boundary considered as x2+y2 = 27 and not x2+y2+z2 = 27 ?
Thanks.

anonymous · Answer

It is because you explore the function $$f(x,y)=x ^{3}+y ^{3}-(27-x ^{2}-y ^{2})^{\frac{ 3 }{ 2 }}$$ which is a function of 2 varibles. The function is defined in the region where $$x ^{2}+y ^{2} \le 27$$ because of the square root. The boundries of the region are when $$x ^{2} + y ^{2} = 27$$ . We do not look at 'z' because it dependant from x and y and we have reduced our problem to a function of 2 variables which we investigate.

anonymous · Answer

Thanks!