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

question 168

Essay

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

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Definitions:

Aphasia

A condition that impairs a person's ability to process language, affecting speech, writing, and the ability to understand language.

Hallucination

A sensory experience of something that does not exist outside the mind, often seen in psychiatric conditions like schizophrenia.

Tactile

Relating to or perceptible through the sense of touch.

Auditory

Relating to the sense of hearing or the system involved in the perception of sound.