next we will summarize the definitions of limits and develop the graphing approach to find the limits of functions the idea behind the approach is very simple let's say we have to find the limit of some function as x approaches to some target value first thing we do is use a graphing device to graph this function then depending on the target value we will try to identify one of the familiar patterns and describe it using the language of limits if x approaches to some value a from the left then we will try to identify these three behaviors if x approaches to some value a from the right then we will try to identify these three behaviors if x approaches to some value a from both sides then we will try to identify this three behaviors and if x approaches to negative infinity then we'll try to identify these three behaviors and finally if x approaches to positive infinity then we'll try to identify these three behaviors and if a function doesn't have any of the recognizable behaviors then we'll say the limit doesn't exist as in these three examples we summarized all of the 15 graphing definitions of limits and introduced the graphing approach that allows us to find a limit of any function when a graph of a function is provided or a graphing device is available