Consider the Curve $\vec { r } ( t ) = \left( 5 t ^ { 2 } + 1 \right) \vec { i } + \left( t ^ { 2 } - 5 \right) \vec { j } + t \vec { k }$

question 81

Essay

Consider the curve $\vec { r } ( t ) = \left( 5 t ^ { 2 } + 1 \right) \vec { i } + \left( t ^ { 2 } - 5 \right) \vec { j } + t \vec { k }$ Find the equation of the tangent line at the point where t = 2.

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Definitions:

Induced Consumption

Consumer spending that increases as disposable income rises, and decreases as disposable income falls, unrelated to the level of interest rates.

Wealth Effect

The change in spending that accompanies a change in perceived wealth, typically when home values or investment portfolios increase.

Induced Consumption

Describes consumer spending that increases when income increases and decreases when income decreases, directly related to the level of disposable income.

Average Propensity

The proportion of total income or revenue that is spent on a certain category of expenditures or savings.