Question

Find the limit, if it exists, of lim (x, y)→(4, 0) ln(16y² / x² + xy)?

Answer 1

The limit of the given function as (x, y) approaches (4, 0) does not exist.

Step-by-step explanation:

To find the limit of the given function, we can use the concept of limits as (x, y) approaches a specific point. In this case, we are interested in the limit as (x, y) approaches (4, 0). We need to substitute the given values into the function and simplify:

ln(16y² / x² + xy) = ln(16(0)² / 4² + 4(0)) = ln(0)

The natural logarithm of zero is undefined, so the limit does not exist.