Question

Determine the set of points at which the function f(x, y) = ex²y * y⁴ is continuous.

Answer 1

The function f(x, y) = ex²y * y⁴ is continuous for all values of x and y.

Step-by-step explanation:

To determine the set of points at which the function f(x, y) = ex²y * y⁴ is continuous, we need to consider two conditions:

1. The function y(x) must be continuous.
2. The first derivative of y(x) with respect to space, dy(x)/dx, must be continuous, unless V(x) = ∞.

By analyzing the given function, we can see that both e^x and x^n (where n is a constant) are continuous functions. Therefore, f(x, y) will be continuous for all values of x and y.