Provide an Appropriate Response $r = 4 \tan \theta , 0 \leq \theta \leq 2 \pi$

question 11

Essay

Provide an appropriate response.
-Find any horizontal or vertical asymptotes for the curve $r = 4 \tan \theta , 0 \leq \theta \leq 2 \pi$ . (Suggestion: Express the curve in parametric form $( \mathrm { x } = \mathrm { r } \cos \theta , \mathrm { y } = \mathrm { r } \sin \theta )$ and investigate what happens to $\mathrm { x }$ and $\mathrm { y }$ as $\theta$ varies.)

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Definitions:

Euglenoids

Single-celled organisms found in freshwater environments, characterized by their elongated shapes and the presence of a flagellum for movement.

Gut-dwelling

Referring to organisms that live within the digestive tract of a host, contributing to or affecting the host's health and nutritional status.

Ciliates

Single-celled or colonial protists with cilia.

Cellulose

A complex carbohydrate comprised of glucose units, forming the primary structural component of plant cell walls.