Is the exponential function continuous in R^n? How can one show this? Let's say for a function like f:R^2->R,f(x,y)=x^y.

Lisantiom 2022-10-05 Answered
Is the exponential function continuous in R n ? How can one show this? Let's say for a function like f : R 2 R , f ( x , y ) = x y
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Johnny Parrish
Answered 2022-10-06 Author has 12 answers
The domain is not the entire R 2 , as we have trouble with negative values of x. If x>0, we have that x y = e y log x , which is continuous because the one-variable exponential and ( x , y ) y log x are continuous.
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