find the limit: lim of f(x) as x approaches 1 if f(x) = x^2 + 4, x is not equal to one and 2, x = 1.

What is the answer and why?

To find the limit of a function as x approaches a specific value, we need to determine the behavior of the function as x gets arbitrarily close to that value. In this case, we want to find the limit of f(x) as x approaches 1.

First, let's evaluate the function at x = 1. For x = 1, f(x) = (1)^2 + 4 = 1 + 4 = 5. Hence, f(1) = 5.

Next, let's examine the function f(x) for values of x that are close to but not equal to 1. As stated in the problem, f(x) = x^2 + 4 for x not equal to one and two. When x is close to but not equal to 1, the behavior of the function can be understood by evaluating the function expression x^2 + 4.

Taking the limit as x approaches 1, we have to consider the behavior of the function as x gets arbitrarily close to 1. Since f(x) is a polynomial function (x^2 + 4), there are no asymptotes or restrictions on the function. Therefore, the limit of f(x) as x approaches 1 exists and can be found by evaluating the function as x gets arbitrarily close to 1.

Hence, the limit of f(x) as x approaches 1 is 5, which is the same value as the function evaluated at x = 1 (f(1) = 5).

In conclusion, the answer is 5.