Let

question 26

Essay

Let .
A) Do and exist? If so, find them.
B) Use the definition of directional derivative to compute for .
C) Examine whether holds, and conclude the differentiability of at the origin.

• A) Do and exist? If so, find them.
• B) Use the definition of directional derivative to compute for .
• C) Examine whether holds, and conclude the differentiability of at the origin.

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Definitions:

Monopolistically Competitive

A marketplace configuration in which a wide variety of firms supply products that are analogous but not identical, thereby granting them a modicum of market influence.

Elastic

A characteristic of goods where their demand or supply changes significantly when the price changes.

Monopolistic Competitor

A market structure where many firms offer products or services that are similar but not perfect substitutes, allowing for some degree of market power.

Excess Capacity

describes a situation where a firm produces less than its total output capacity, usually resulting in inefficiencies and higher production costs.