Consider Where Is $f$ Continuous

question 238

Essay

Consider $f ( x , y ) = \left\{ \begin{array} { l l } \frac { x ^ { 4 } - y ^ { 4 } } { x ^ { 2 } + y ^ { 2 } } & \text { if } ( x , y ) \neq ( 0,0 ) \\0.1 & \text { if } ( x , y ) = ( 0,0 )\end{array} \right.$ Where is $f$ continuous?

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Definitions:

Adolescent

An adolescent is an individual in the transition phase between childhood and adulthood, typically between the ages of 13 and 19, characterized by significant physical, psychological, and social changes.

Peer Groups

Social groups consisting of individuals of similar age and status, which influence behaviors, values, and attitudes.

Adolescent Clique

An Adolescent Clique is a small, close-knit group of teenagers sharing similar interests or social status, often excluding outsiders.

Dunphy

A surname associated with various individuals and may refer to Desmond Dunphy's study on adolescent social structures but without specific context, it's too broad to define precisely.