Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

question 197

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where S is the boundary surface of the region outside the sphere $\mathrm { x } ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$ and inside the ball $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 4$ and $\mathbf { F } = e ^ { y ^ { 2 } } \mathbf { i } + \left( 5 y + e ^ { x ^ { 2 } } \right) \mathbf { j } + ( - 3 z + 2 x ) \mathbf { k }$ .

Grasp the notion of marginal analysis and how it is applied to make decisions.

Recognize the role of scarcity in economics and how it necessitates choices.

Apply the economic perspective to analyze individual and societal choices.

Discern the difference between rational and irrational behavior in the context of economics.

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Definitions:

Compounded Quarterly

Related to the calculation of interest which is added to the principal amount at the end of every quarter, or every three months.

Preferred Share

A class of ownership in a corporation with a higher claim on assets and earnings than common stock, often receiving dividends before common shareholders.

Discount Rate

The interest rate that the Federal Reserve charges commercial banks for loans, or a rate used in discounted cash flow analysis to determine the present value of future cash flows.

Compounded Semi-annually

Interest calculation method where the interest is added to the principal twice a year, leading to a growth in the amount at a faster rate than simple interest.