Place the linear equation into limit notation with respect to the limit being evaluated. For example the equation f (x) = 1 / x becomes Lim (x -> 0) 1 / x. This notation is spoken, "the limit as x approaches zero of 1 / x."
Substitute the limit value into the equation and evaluate the equation. This is the easiest method for evaluating a limit, however, it does not always yield a result. Given our example, substituting zero yields 1 / 0 which is undefined in mathematics.
Examine the values returned by the function from both the left and right side of the limit value. In our example, the values returned as you approach 1 / 0 from the left increases without bound toward negative infinity. When approaching from the right the values grow without bound toward positive infinity.
Determine if the general limit exists. For a general limit to exist the function must approach the same value when approaching from either the left or right side. Concluding the example, the linear function 1 / x does not possess a limit.