Find Two Paths of Approach from Which One Can Conclude $\text { Show that } f ( x , y , z ) = e ^ { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \text { is continuous at the origin. }$

question 229

Essay

Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0).
- $\text { Show that } f ( x , y , z ) = e ^ { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \text { is continuous at the origin. }$

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Definitions:

Four-Firm Concentration Ratio

A metric that measures the total market share held by the top four firms within a specific industry, indicating the level of market concentration.

Herfindahl Index

A measure of market concentration used to determine the competitiveness of an industry, calculated by squaring the market share of each firm competing in the market.

Oligopoly

A market structure characterized by a small number of firms that dominate the market, leading to limited competition and potential for collusion.

General Rule

An established guideline or principle that is generally followed or considered as a norm in a particular field or situation.