Find the Arc Length Function $s ( t )$ For the Curve Defined By

question 94

Essay

Find the arc length function $s ( t )$ for the curve defined by $\mathbf { r } ( t ) = e ^ { 2 t } \cos t \mathbf { i } + e ^ { 2 t } \sin t \mathbf { j } + e ^ { 2 t } \mathbf { k }$ for $t \geq 0$ . Then use this result to find a parametrization of $C$ in terms of $s$ .

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Definitions:

Sexual Maturity

The stage in an organism's life cycle when it becomes capable of reproduction.

Vulnerable

A state of being susceptible to harm or damage, often used to describe species at risk of extinction or ecosystems facing threats.

Population Size

Population Size indicates the total number of individuals or units within a specified area or population group at a given time.

Ability

The capacity, skill, or proficiency to do something effectively.