Consider the Top Half of the Ellipsoid $x ^ { 2 } + y ^ { 2 } + \frac { 1 } { 4 } z ^ { 2 } = 1 , z \geq 0$

question 137

Short Answer

Consider the top half of the ellipsoid $x ^ { 2 } + y ^ { 2 } + \frac { 1 } { 4 } z ^ { 2 } = 1 , z \geq 0$ parametrized by $x = \sin u \sin v , y = \cos u \sin v , z = 2 \cos v , 0 \leq v \leq \frac { \pi } { 2 }$ . Find a normal vector N at the point determined by $u = \frac { \pi } { 4 } , v = \frac { \pi } { 3 }$ , and determine if it is upward and/or outward.

---

Definitions:

Unresolved Issues

Refers to ongoing personal, social, or emotional problems that have not been adequately addressed or resolved.

Personal Counseling

A form of psychological support aimed at helping individuals address personal, social, or psychological challenges.

Supervision

The act of directing, overseeing, and monitoring the performance of individuals or groups to ensure that goals and standards are met.

Unresolved Grief

A prolonged and complex form of grief where the process of mourning is inhibited or stalled, leading to continued distress or dysfunction.