If $z = f ( x , y )$ Has Continuous Second Partial Derivatives

question 1

Essay

If $z = f ( x , y )$ has continuous second partial derivatives, $x = 2 u + v$ , and $y = u - 3 v$ , express $\frac { \delta ^ { 2 } z } { \delta u \delta v }$ in terms of $\frac { \delta ^ { 2 } z } { \delta x ^ { 2 } }$ , $\frac { \delta ^ { 2 } z } { \delta x \delta y }$ , and $\frac { \delta ^ { 2 } z } { \delta y ^ { 2 } }$ .

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Foreign Assets

Investments or properties owned by individuals, companies, or governments in countries other than their own.

Trade Balance

The difference in value between a country's imports and exports over a certain period, indicating the relative strength of its economy.

Net Capital Outflow

The sum representing a country's outbound investments minus its inbound investments from abroad over a specific period.

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The allocation of resources, such as capital or time, in expectation of future benefit or profit.