Let $\mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$

question 71

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and let S be the boundary surface of the solid $E = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 1 \right\}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

• A) \(0\)
• B) \(\frac { \pi } { 2 }\)
• C) \(\pi\)
• D) \(\frac { 4 \pi } { 3 }\)
• E) \(\frac { 2 \pi } { 3 }\)
• F) \(\frac { 8 \pi } { 3 }\)
• G) \(2 \pi\)
• H) \(4 \pi\)

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Definitions:

Exchange Gain

The profit resulting from foreign exchange transactions and the fluctuation in exchange rates, realizing a higher value in the home currency.

Net Loss

The amount by which total expenses exceed total revenues for a business during a specific period, indicating a financial loss.

Spot Rate

The current exchange rate at which a currency can be bought or sold for immediate delivery.

Exchange Gains

arise from holding foreign currencies and result from favorable changes in exchange rates, leading to an increase in the domestic currency value of the foreign currencies held.