f(x) = x2 + 3x - 1
f(1) = 12 + 3*1 - 1
f(1) = 3So, the value of the function at x = 1 is called its limit at x = 1. This is written as
lim x → 1x2 + 3x - 1 = 3
Not all functions have a specific y value for a specific x-value, as the above one. In such functions, the limit is taken as the y-value around towards which the graph is approaching from both sides of the x value. For example, the graph of the following function does not exist at x = 1. But, looking at its graph, you can tell that it is approaching y = 10 when you move in nearer and nearer to x = 1. Thus, although the value of the function does not exist at x = 1, its limit is said to be equal to 10 as x approaches 1.