Use-polar-coordinate-to-find-lim-x-y-0-0-y-2-x-2-y-2-

Question Number 187611 by otchereabdullai last updated on 19/Feb/23

U s e p o l a r c o o r d i n a t e t o f i n d

l i m (x, y) \to (0, 0) \frac{y^{2}}{x^{2} + y^{2}}

Answered by mahdipoor last updated on 19/Feb/23

n o t e x i s t

g e t y = 0 a n d x \to 0 \Rightarrow l i m = \frac{0}{x^{2} + 0} = 0

g e t y \to 0 a n d x = 0 \Rightarrow l i m = \frac{y^{2}}{0 + y^{2}} = 1

g e t (y = x) \to 0 \Rightarrow l i m = \frac{x^{2}}{x^{2} + x^{2}} = \frac{1}{2}

\dots

Answered by a.lgnaoui last updated on 19/Feb/23

I t h i n k t h a t a r u l e o f l h o p i t a l

c a n g e t a s o l u t i i n

f (x) = x^{2} + y^{2} g (x) = y^{2}

{l i m}_{x \to a} (\frac{f}{g}) = {l i m}_{x \to a} (\frac{f^{'}}{g^{^{'}}})

w i t h \frac{d (x^{2} + y^{2})}{d (x, y)} = ?