Unbounded limits

so right over here we have the graph of y is equal to one over x squared and my question to you is what is the limit of 1 over x squared as X approaches zero pause this video and see if you can figure that out well when you try to figure it out you immediately see something interesting happening at x equals zero the closer we get to zero from the left you take 1 over x squared it just gets larger and larger and larger it doesn't approach some finite value it's unbounded has no bound and the same thing is happening as we approach from the right as we get values closer and closer to zero from the right we get larger and larger values for 1 over x squared without bound so terminology that folks will sometimes use where they're both going in the same direction but it's unbounded as they'll say this limit is unbounded in some context you might hear teachers say that this limit does not exist or and it definitely does not exist if you're thinking about approaching a finite value in future videos we'll start to introduce ideas of infinity and notations around limits and infinity where we can get a little bit more specific about what type of limit this is but with that out of the way let's look at another scenario this right over here you might recognize as the graph of y is equal to 1 over X so I'm going to ask you the same question pause this video and think about what's the limit of 1 over X as X approaches 0 pause this video and figure it out alright so here would we approach from the left we get more and more and more negative values while we when we approach from the right we're getting more and more positive values so in this situation where we're not getting unbounded in the same direction the previous example we were both we were being unbounded in the positive direction but here on though from the left we're getting unbounded in the negative direction while from the right we're getting unbounded in the positive direction and so when you're thinking about the limit as you approach a point if it's not even approaching the same value or even the same direction you would just clearly say that this limit does not exist does not exist so this is a situation where you would not even say that this is an unbounded limit or that the limit is unbounded because you're going in two different directions when you're approached from the right and when you approach from the left you would just clearly say does not exist