Using the Divergence Theorem, Find the Outward Flux of F $\mathbf { F } = x y \mathbf { i } + \mathrm { y } ^ { 2 } \mathbf { j } - 2 y z \mathbf { k }$

question 257

Multiple Choice

Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.
- $\mathbf { F } = x y \mathbf { i } + \mathrm { y } ^ { 2 } \mathbf { j } - 2 y z \mathbf { k }$ ; $\mathrm { D }$ : the solid wedge cut from the first quadrant by the plane $\mathrm { y } + \mathrm { z } = 2$ and the parabolic cylinder $x = 1 - 16 y ^ { 2 }$

• A) \(\frac { 29 } { 960 }\)
• B) \(\frac { 7 } { 240 }\)
• C) \(\frac { 7 } { 120 }\)
• D) \(\frac { 1 } { 30 }\)

---

Definitions:

Present Value

The present value of a future amount of money or series of cash flows, assuming a certain return rate.

Replacement Cost

The current cost of replacing an asset with a new one of similar kind and quality, used in accounting to value assets.

Settlement Amount

A financial sum agreed upon by parties in a contract, often referring to the resolution amount in disputes or the completion payment in transactions.

Retained Earnings

The portion of net earnings not paid out as dividends but retained by the company to be reinvested in its core business or to pay debt.