Calculating the Limit of a Function - Calculus Help

1.) Calculate Left hand limits and Right hand limits. 2.) If they are the same, then limit exists. 3.) If they are different, then limit doesn't exist. You can't exactly substitute the same number "x" because x is tending to a certain value and is not that value.

Well, limits aren't always as simple as subbing in x. There are some problems that are that easy, but what a limit really means is the value the function approaches as x approaches a certain number. It's not the value of the function when x is at a certain number, but the value when x approaches that number. So, if you have a graph that looks like this: 6 . | |.. ...... | ---|--------- | 2 | | The value at x=2 might be 6, but the limit as x approaches 2 would be the y value of the straight line. If the limit doesn't exist, the graph will often look something like this: | ........ | |.. | ---|-------- | 2 | | In this case, you have to calculate both the left hand and right hand limits (or the limit as the x approaches from the left and the right). Here, the left hand limit is the y-value of the lower line (say 3) and the right hand limit is the y-value of the upper line (say 6). Since they don't match, the limit doesn't exist.

Calculating d limits of a function r sumtimes not easier, dey r a bit tricky. Firstly, u hv 2 keep in mind d different formulas of limits & den try 2 convert ur function 2 either of dem. Moreover, a limit's said 2 b non-existing when LHL & RHL of F(x) are unequal. LHL is found wid lim x- while RHL's determined by applying lim x+. Ask if wid d exact problem next time if u don't get d result easily.