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limit as (x,y) approaches (0,0) of (xy)/(x^2+y^2)

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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lim_{(x, y)→ (0, 0)}(xyx²+y² )

Solution

diverges

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lim_{(x, y)→ (0, 0)}(xyx²+y² )

Find two different paths to approach the point that gives different values for the limit

Limit of lim_{(x, y)→ (0, 0)}(xyx²+y² ) along x=0: 0

Limit of lim_{(x, y)→ (0, 0)}(xyx²+y² ) along x=y: 12

=diverges

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

limit as (x,y) approaches (0,0) of (xy)/(x^2+y^2)

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