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## Homework Statement

f(x,y) is a hybrid function

1. ( ( xy+x )^3 ) / ( x^2 + xy ) when (x,y) not equal to (0,0)

2. 0......................................when (x,y) = (0,0)

Is this function continuous at the origin?

## Homework Equations

.......lim.......df |(x,y) = df(0,0)

(x,y)->(0,0)

## The Attempt at a Solution

To determine this I have to use the continuity Rule (above) and first principle.

so

lim....f(0,h) - F(0)........(Imagine the divisor line there)

h->0.........h..............(and excuse the dots, spaces don't work)

=

lim.....[x(y+x^2) - 0 ] x [ 1 ]

h->0..[...x(x+y).......]....[ h ]

................^

From here I'm a little stuck.

Do I cancel the x and solve the limit which result in infinity and therefore the function is not continuous at the origin OR put in the value of (0,h) for (x,y) and get the limit to equal zero?

ie.

....lim.....[0(h+0) - 0 ] x [ 1 ]

....h->0..[...0(0+h).....]....[ h ]

..=lim...........1

....h->0 .......h