The limit of a given function f(x), is a tool for investigating the behavior of f(x) as x gets closer to a particular numberX0 = C. In order to guess the value of given limit limx_,cf(x)=L We can evaluate in the given function values closer to $x=c$ from the left and from the right of it. This procedure gives us an idea of the limit if it exists. Neverthelessl this procedure does not give us a conclusive result. Usually the procedure is complicated, and then some rules are used to evaluate the limit. For example, if $f(x) is a polynomial function then lim f(x)=f(c) X114: Find the limit by plugging in the x value This technique for algebraically solving for a limit is to plug the number that x is approaching into the function. If you get an undefined value (0 in the denominator), you must move on to another technique. But if your function is continuous at that x value, you will get a value, and you're done; you've found your limit! For example, with this method, you can find this limit: "I." x2 6X+8 :45 x4 The limit is 3, because f(5) = 3 and this function is continuous at x = 5