I have a question.
Show, by using the arithmetic rules, that the function g on R2 + deﬁned by
g(x,y) = (ln(1 + x2 + y2),ln(1 + x3y))
is continuous.
How can I do this? I have no idea how to start.
Thank you
exists only for and for the logarithm is continuous. is continuous everywhere, so is continuous everywhere it is defined. (What results have I used there?)
If you can now show that exists and is continuous on , you will have that both and are continuous. What does that mean for ?