Question

for what values of (x,y) is the function f(x,y)=(x^3+7xy^5-8y^6 )/ ( x^2-y^2) continuous

Answer 1

looking at the denominator.

x^2 - y^2 cannot equal zero...

so find the values that x can't be... and the curve would be continuous everywhere else..,

Answer 2

then what is the solve?

Answer 3

well you look at

\[x^2 \neq y^2\]

so

\[x \neq \pm y\]

if x = y then you will have a zero denominator which is undefined..

Answer 4

oh thanks for help