next we will introduce the two-sided infinite limits as a part of the introduction we will discuss the definitions interpretations and a few examples we associate the following behavior near vertical asymptote x equals a with the following limit statement called a two-sided infinite limit we say f approaches to positive infinity as x approaches to a from both sides frequently we emit the plus minus notation and simply say f approaches to positive infinity as x approaches 2a we associate the following behavior near vertical asymptote x equals a with the following limit statement called a two-sided infinite limit we say f approaches to negative infinity as x approaches 2 a from both sides frequently we omit the plus minus notation and simply say f approaches to negative infinity as x approaches to a now if for whatever reason the left and the right sided limits do not match or function doesn't exist on either side then we say that the two-sided limit doesn't exist and simply write tne so to interpret the two-sided infinite limits we would first read it as f approaches to positive or negative infinity as x approaches 2 a from both sides next we would mark the asymptote x equals a on the coordinate plane and then draw the behavior according to the statement for instance this is what one would imagine when seeing the following limit statement it shows that f approaches to negative infinity as x approaches to 2 from both sides similarly this is what one would imagine when seeing the following limit statement it shows that f approaches to positive infinity as x approaches to negative 1 from both sides let's do an example consider a function defined by the following graph and let's find the following limits in other words let's describe the behavior of the graph around its vertical asymptotes to find the limit we need to determine whether the function goes up or down on both sides of the asymptote at x equals negative seven it is easy to see that the function approaches negative infinity on both sides in other words f approaches to negative infinity as x approaches to negative 7 from both sides therefore the answer is negative infinity to find the next limit we need to determine whether the function goes up or down on both sides of the asymptote at x equals negative 3. it is easy to see that the function approaches positive infinity on both sides in other words f approaches to positive infinity as x approaches to negative 3 from both sides therefore the answer is plus infinity to find the next limit we need to determine whether the function goes up or down from both sides of the asymptote x equals zero it is easy to see that the function approaches positive infinity on both sides in other words f approaches to positive infinity as x approaches to zero from both sides therefore the answer is positive infinity finally to find the last limit we need to determine whether the function goes up or down from both sides of the asymptote x equals six it is easy to see that the function approaches negative infinity from the left and positive infinity from the right since the two one-sided limits are not matching we say that the two-sided limit doesn't exist we discussed the definitions of two-sided infinite limits using the graphing approach