MAN: Evaluate the following limit the limit as xy approaches the ordered pair 5 comma negative 2 of the function the square root of 29 minus x squared minus y squared and the square root. First, I want to note that the domain of this function is the set of ordered pairs xy such that x squared plus y squared is less than or equal to 29. It is a circle with a radius centered at the origin of the radius of the square root of 29. So 5 comma negative 2, that ordered pair is in our domain. Also this is a continuous function. So the square root function is continuous x squared is continuous y squared is continuous. So this is a continuous function.

So to find our limit all we need to do is evaluate, but we're going to apply some limit laws. So this limit, I'm just going to say that original function limit equals L. So L equals the square root of the limit as xy approaches 5 negative 2 of 29 minus the limit as xy approaches 5 negative 2 of x squared minus the limit as xy approaches negative 2 of y squared. And all of that is underneath our radical. And those limits separately are 29, 25, and 4. So our limit is equal to the square root of 29 minus 25 minus 4, which is equal to 0.