 But it is also often useful to be able to define the limit of a function at some particular finite real-valued input. For instance, we might be interested in the function \(f(x)=\frac{x^2-9}{x-3}\) as \(x\) approaches 3. (As we will see in section  3.4,  this sort of calculation is particularly important in defining the concept of ‘derivative’ of a function, giving the slope of a continuous curve at a point.) This particular function is defined for all real numbers other than 3, and at any such input \(x\) it takes the value \(x+3\). We would like to be able to say that the limit of this function as \(x\) approaches 3 is 6. The way we make this precise is to say that 