What Value of C (If Any)makes the Following Function Continuous

question 8

Short Answer

What value of c (if any)makes the following function continuous at (0, 0)? $$f ( x , y ) = \left\{ \begin{array} { c c } \frac { x ^ { 4 } - y ^ { 4 } } { x - y } & \text { if } ( x , y ) \neq ( 0,0 ) \\c & \text { otherwise }\end{array} \right.$$

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Definitions:

Relativistic Thinking

A type of thinking that recognizes the validity of multiple perspectives and that knowledge is contextual rather than absolute.

Dualism

A philosophical concept that posits the existence of two fundamental principles, often mind and body, as separate and fundamentally different in nature.

Relativistic

In cognitive development, the understanding that knowledge and truth can vary depending on context or perspective, rather than being absolute.

Reflective

Characterized by deep thought or the careful consideration of past experiences, actions, or feelings.