Question

(f(x, y)=(xy)(1+e((ˣ⁻ʸ)))) where is it continuous?

a) Everywhere
b) Nowhere
c) Continuous at ((0,0))
d) Continuous at ((1,1))

Answer 1

The function f(x, y) = (xy)(1+e^{(x-y)}) is continuous everywhere, as it is composed of continuous functions (xy), 1, and e^{(x-y)}, hence the answer is (a) Everywhere.

Step-by-step explanation:

The question asks to determine where the function f(x, y) = (xy)(1+e^{(x-y)}) is continuous. A function of two variables is continuous at a point if the limit as you approach that point is equal to the function value at that point. For this function, the product xy, the constant 1, and the exponential function e^{(x-y)} are all known to be continuous everywhere on their domains.

Since the function is composed of the multiplication and addition of continuous functions, it follows that f(x, y) is continuous everywhere on its domain. Therefore, the correct answer is that f(x,y) is continuous everywhere.