The limit lim_((x,y) => (0,0)) (x^3 y)/(x^6 + y^2)

Darryl English

Darryl English

Answered question

2022-07-23

The limit
L = lim ( x , y ) ( 0 , 0 ) x 3 y x 6 + y 2
Is equal to zero if y is any polynomial except y = m x 3 ,   x R
Is the claim true?

Answer & Explanation

Mira Spears

Mira Spears

Beginner2022-07-24Added 14 answers

It's not true. Take for example y = x 3 + x 4 . Then
f ( x , y ) = 1 + x 2 + 2 x + x 2
and the limit along that curve will be 1/2.

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