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

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Essay

Find the unit tangent and unit normal vectors T(t)\mathrm { T } ( t ) and N(t)\mathrm { N } ( t ) for the curve CC defined by r(t)=ti+2t2j\mathbf { r } ( t ) = t \mathbf { i } + 2 t ^ { 2 } \mathbf { j } . Sketch the graph of CC , and show T(t)\mathrm { T } ( t ) and N(t)\mathrm { N } ( t ) for t=1t = 1 .

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Definitions:

Normal Populations

Populations that follow a normal distribution, where the majority of data points are concentrated around the mean value.

Standard Error

A statistical term that measures the accuracy with which a sample distributes around the population mean; it is the standard deviation of the sampling distribution.

Sampling Distribution

The probability distribution of a given statistic based on a random sample, used to estimate population parameters.

Formal Charge

Used to calculate the charge of an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms.

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