Use Stokes' Theorem to Evaluate $\iint _ { S } \operatorname { cur } \mathbf { F } \cdot d \mathbf { S }$

question 7

Short Answer

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { cur } \mathbf { F } \cdot d \mathbf { S }$ .
$$\mathbf { F } ( x , y , z ) = 9 x y \mathbf { i } + 6 y z \mathbf { j } + 9 z ^ { 2 } \mathbf { k }$$ $S$ is the part of the ellipsoid $4 x ^ { 2 } + 4 y ^ { 2 } + 49 z ^ { 2 } = 196$ lying above the $x y$ -plane and oriented with normal pointing upward.

---

Definitions:

Pure Exchange Economy

An economic model where there is no production, and agents trade endowments of goods that they own initially.

Utility Function

A mathematical representation of how consumers rank different bundles of goods according to the levels of satisfaction those goods provide.

Numeraire

A standard unit of account in economics used to compare the value of goods and services.

Perfect Substitutes

Goods that a consumer is completely indifferent between, meaning they will substitute one for another at a constant rate regardless of any change in price or utility.