Find the Unit Tangent and Unit Normal Vectors $\mathrm { T } ( t )$

question 159

Essay

Find the unit tangent and unit normal vectors $\mathrm { T } ( t )$ and $\mathrm { N } ( t )$ for the curve $C$ defined by $\mathbf { r } ( t ) = t \mathbf { i } + 2 t ^ { 2 } \mathbf { j }$ . Sketch the graph of $C$ , and show $\mathbf { T } ( t )$ and $N ( t )$ for $t = 1$ .

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Definitions:

Urban Cluster

A densely populated area that has a total population of less than 50,000 people.

Economic Integration

The process by which countries reduce trade and investment barriers to create closer economic cooperation or amalgamation.

Census Bureau

A government agency responsible for collecting, analyzing, and publishing statistical data on the population, economy, and society of a country to aid in policy-making and administration.

Population Decline

A decrease in the number of inhabitants of a given area, which could result from factors like decreasing birth rates, increasing death rates, or migration.