## University Calculus: Early Transcendentals (3rd 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) We can not take the square root of a negative value. Hence, $4-x^2-y^2-z^2\ge 0$. Thus, for all (x,y,z) such that $x^2+y^2+z^2 \le 4$ b) There must not be zero in the denominator. Also, we can not take the square root of a negative number. Thus, $x^2+y^2+z^2-9\ge 0$ And, $4-\sqrt{x^2+y^2+z^2-9}\ne 0$ So, for all $(x,y,z )$ such that $x^2+y^2+z^2 \ge 9$ except when $x^2+y^2+z^2=25$