What is the limit as (x,y) approaches (0,0) of (2x)/(x^2+x+y^2) ?

The limit as (x,y) approaches (0,0) of (2x)/(x^2+x+y^2) is diverges

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

(x, y) \to (0, 0) lim (\frac{2 x}{x ^{2} + x + y ^{2}})

diverges

Solution steps

(x, y) \to (0, 0) lim (\frac{2 x}{x ^{2} + x + y ^{2}})

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

Limit of

(x, y) \to (0, 0) lim (\frac{2 x}{x ^{2} + x + y ^{2}})

along

x = 0 : 0

Limit of

(x, y) \to (0, 0) lim (\frac{2 x}{x ^{2} + x + y ^{2}})

along

x = y : 2

= diverges

\int \frac{3 x + 5}{x ^{3} - x ^{2} - x + 1} d x

\frac{d}{d x} (arctan (sin (x^{2} + \frac{π}{x})))

y^{^{''}} + y^{^{'}} + y = t

\frac{d}{d x} (6 x^{2} - 4 x)

y^{^{''}} + 5 y = 0, y^{^{'}} (1) = 5

What is the limit as (x,y) approaches (0,0) of (2x)/(x^2+x+y^2) ?
The limit as (x,y) approaches (0,0) of (2x)/(x^2+x+y^2) is diverges