Evaluate $\iint _ { S } f ( x , y , z ) d S$

question 67

Multiple Choice

Evaluate $\iint _ { S } f ( x , y , z ) d S$ . $f ( x , y , z ) = z$ ; S is the part of the torus with vector representation $\mathbf { r } ( u , v ) = ( 5 + 3 \cos v ) \cos u \mathbf { i } + ( 5 + 3 \cos v ) \sin u \mathbf { j } + 3 \sin v \mathbf { k }$ , $0 \leq u \leq 2 \pi$ , $0 \leq v \leq \frac { \pi } { 2 }$ .

• A) 0
• B) \(117 \pi\)
• C) \(117\)
• D) \(27 \pi\)

---

Definitions:

Stock Options

Contracts that grant the holder the right, but not the obligation, to buy or sell a stock at a predetermined price within a specific time frame.

Available-for-Sale

Available-for-sale refers to financial assets that are not classified as held-for-trading or held-to-maturity, and are recorded at fair value with changes recognized in other comprehensive income.

Market Values

The current price at which an asset or service can be bought or sold in a competitive marketplace.