Question

Give an example of a two variable function that is not continuous at (1,2) . Explain why your example works.

Answer 1

A two-variable function is something like:

z = f(x, y).

We want this function to not be continuous at (1, 2), this means that x = 1 and y = 2.

Now, a easy way to make a function not continuous at a given point, we can have a denominator that is equal to zero at that particular point, and this is because we can not divide by zero

For example, we could have:

`f(x, y) = (1)/((x - 1) + (y - 2))`

The denominator is (x - 1) + (y - 2)

When x = 1, and y = 2, this is equal to zero, then this function is not continuous in the point (1, 2).