Let And Let S Be the Surface with Equation $x ^ { 4 } + y ^ { 4 } + z ^ { 4 } = 1$

question 65

Short Answer

Let $\mathbf { F } ( x , y , z ) = \left( x + e ^ { y \tan z } \right) \mathrm { i } + 3 \mathrm { xe } ^ { x z } \mathbf { j } + ( \cos y - z ) \mathbf { k }$ and let S be the surface with equation $x ^ { 4 } + y ^ { 4 } + z ^ { 4 } = 1$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

---

Definitions:

Non-Controlling Interest

A financial interest in a subsidiary not attributed to the parent company, representing minority shareholders' equity in the subsidiary's net assets.

Bonds Payable

Long-term liabilities representing money owed by a corporation or government to bondholders, to be repaid at a specific future date.

Straight Line Amortization

A method of amortizing an intangible asset evenly over its useful life.

Voting Shares

Equity that grants the investor voting privileges on matters like board of directors' elections.