Find Two Paths of Approach from Which One Can Conclude $$f ( x , y ) = \frac { x ^ { 2 } y } { x ^ { 4 } + y ^ { 2 } }$$

question 149

Essay

Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0).
- $$f ( x , y ) = \frac { x ^ { 2 } y } { x ^ { 4 } + y ^ { 2 } }$$

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Definitions:

Positional Cues

Visual or auditory signals that allow individuals to determine their spatial relationship with their environment or other entities within it.

Facial Expressions

Visible changes in the face that convey emotional states, intentions, or reactions to stimuli, serving as crucial components of nonverbal communication.

Phony Smile

A forced or insincere smile, often used to hide one's true feelings or to socially conform.

Complex Expressions

Phrases or sentences that combine multiple elements such as operators, variables, and constants to convey a specific calculation or idea.