Let $S$ Be the Cube with Vertices $( \pm 1 , \pm 1 , \pm 1 )$

question 10

Short Answer

Let $S$ be the cube with vertices $( \pm 1 , \pm 1 , \pm 1 )$ . Approximate $\iint _ { S } \sqrt { x ^ { 2 } + 2 y ^ { 2 } + 7 z ^ { 2 } }$ by using a
Riemann sum as in Definition 1, taking the patches $S _ { y j }$ to be the squares that are the faces of the cube and the points $P _ { i j }$ to be the centers of the squares.

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Definitions:

Leisure Time

Free time that an individual can spend away from work, chores, and other obligatory activities, often used for rest, recreation, or personal interests.

Value Added

Value Added refers to the increase in value that a business creates by undergoing a production process, calculated as the difference between the cost of raw materials and the price of the finished product.

Income Approach

A method of calculating GDP that sums up total national income, including wages, rent, interest, and profits.

Consumer Price Index (CPI)

An indicator used to gauge inflation by examining the weighted average prices of a selection of consumer products and services.