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

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

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limit as (x,y) approaches (0,0) of x^y

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

diverges

Solution steps

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

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

Limit of

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

along

x = 0 : 0

Limit of

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

along

y = 0 : 1

= diverges

x \to 2 lim (7 - 2 x)

\int \frac{x}{x ^{4} + 9} d x

\int \frac{x + 4}{x ^{2} + 2 x + 5} d x

\int_{0}^{2} x d x

f (x) = - 3 x^{3} - 3 x^{2} - x + 3, at x = - 1

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