Find Two Paths of Approach from Which One Can Conclude

question 212

Essay

Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0).
- $\text { Show that } f ( x , y , z ) = x ^ { 2 } y ^ { 5 } z ^ { 5 } \text { is continuous at every point } \left( x _ { 0 } , y _ { 0 } , z _ { 0 } \right) \text {. }$

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Definitions:

Behaviors

Actions or reactions of an individual in response to external or internal stimuli.

Individual

Pertaining to a single person or thing, as opposed to a group or collective.

Duration of Behavior

The length of time over which a particular behavior or set of behaviors is observed or continues to occur.

Identified Stimulus

A specific environmental cue or event that is recognized and can trigger a particular response.