Find an Equation of the Tangent Plane to the Surface $x = \cos u \sin v$

question 33

Essay

Find an equation of the tangent plane to the surface with parametric equations $x = \cos u \sin v$ , $y = \sin u \sin v$ , $z = \cos v$ at the point $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } , \frac { 1 } { \sqrt { 2 } } \right)$ .

---

Definitions:

Financial Distress

A situation where an individual or company cannot meet or has difficulty paying off its financial obligations to creditors.

Anchored

A cognitive bias where an individual relies too heavily on an initial piece of information (the "anchor") when making subsequent judgments or decisions.

Prospect Theory

A behavioral economic theory that describes how people choose among probabilistic alternatives and assess the risk of loss differently from the potential for gains.

Pricing

The strategy and methodology of determining the selling price of a product or service, taking into account factors like cost, demand, and competition.