Suppose That $x y ^ { 2 } + \sin y + x ^ { 3 } = 8$

question 157

Short Answer

Suppose that $x y ^ { 2 } + \sin y + x ^ { 3 } = 8$ .Evaluate $\frac { d y } { d x }$ and use the result to find the tangent line at the point (2,0).Use this to find an approximate value for y when x = 2.02.

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Definitions:

Cubozoan

A class of box jellyfish known for their cube-shaped medusae and highly venomous stings.

Colony of Polyps

A group of many individual polyps (small, sessile organisms) that are genetically identical and physically connected, often found in corals.

Cnidaria

A phylum of aquatic invertebrate animals that includes jellyfish, corals, and sea anemones, characterized by a simple body plan with radial symmetry.

Nervous System

A complex network of neurons that coordinates body functions and transmits signals between different body parts.