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Sketch the Curve Represented by the Vector-Valued Function r(t)=(4t)i+tj and \mathbf { r } ( t ) = ( 4 - t ) \mathbf { i } + \sqrt { t } \mathbf { j } \text { and }

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Sketch the curve represented by the vector-valued function r(t) =(4t) i+tj and \mathbf { r } ( t ) = ( 4 - t ) \mathbf { i } + \sqrt { t } \mathbf { j } \text { and } give the orientation of the curve.


Definitions:

Substitution Effect

This effect describes the change in consumption patterns due to a change in the relative prices of goods, leading consumers to substitute more expensive items with cheaper ones.

Output Effect

The impact on total output or production resulting from changes in the price level or other economic factors.

Price of Capital

The cost of using capital goods, represented by interest rates, lease payments, or other measures of the cost of borrowing or using capital.

Marginal Revenue Product

The additional revenue generated from employing one additional unit of a resource, such as labor or capital.

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