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:

Nominal Variable

A variable measured in terms of money that has not been adjusted for inflation, reflecting the current price level.

Real Variable

An economic measure that has been adjusted for changes in price level, enabling comparison of quantities across different times.

Excess Supply

A situation where the quantity supplied of a good or service exceeds the quantity demanded at the current price, often leading to a decrease in price.

Money Supply

The full amount of monetary assets in an economy at a particular time, covering cash, coins, and the amounts in checking and savings accounts.