What is the limit as (x,y) approaches (0,0) of ((sin(2x)-2x+y))/(x^3+y) ?

The limit as (x,y) approaches (0,0) of ((sin(2x)-2x+y))/(x^3+y) is diverges

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limit as (x,y) approaches (0,0) of ((sin(2x)-2x+y))/(x^3+y)

(x, y) \to (0, 0) lim (\frac{( sin ( 2 x ) - 2 x + y )}{x ^{3} + y})

diverges

Solution steps

(x, y) \to (0, 0) lim (\frac{sin ( 2 x ) - 2 x + y}{x ^{3} + y})

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

Limit of

(x, y) \to (0, 0) lim (\frac{sin ( 2 x ) - 2 x + y}{x ^{3} + y})

along

x = 0 : 1

Limit of

(x, y) \to (0, 0) lim (\frac{sin ( 2 x ) - 2 x + y}{x ^{3} + y})

along

y = 0 : - \frac{4}{3}

= diverges

\int ln (x) \cdot ln (x) d x

y^{^{''}} x = - 5 sin (8 x)

\frac{\partial}{\partial x} (x ln (z^{7} + x^{5}))

f (x) = (x^{2} + 4 x + 3)^{2}

n = 1 \sum \infty \frac{n}{2 ^{n - 1}}

What is the limit as (x,y) approaches (0,0) of ((sin(2x)-2x+y))/(x^3+y) ?
The limit as (x,y) approaches (0,0) of ((sin(2x)-2x+y))/(x^3+y) is diverges