## Thomas' Calculus 13th Edition

a) For all (x,y,z) such that $x^2+y^2+z^2 \le 4$; b) For all $(x,y,z )$ such that $x^2+y^2+z^2 \ge 9$ except when $x^2+y^2+z^2=25$
a) There is no possible way to take the square root of the negative value.Therefore, $4-x^2-y^2-z^2 \gt 0$ Thus, for all (x,y,z) such that $x^2+y^2+z^2 \le 4$ b) There is no possible way to take the square root of the negative value. and there can be no zero in the denominator. hence,$x^2+y^2+z^2 \ge 9$ and also, $4- \sqrt {x^2+y^2+z^2-9} \gt 0$ Thus, For all $(x,y,z )$ such that $x^2+y^2+z^2 \ge 9$ except when $x^2+y^2+z^2=25$