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Okay let×39’s do l'hospital's rule every no wand then I call them El hospital I don'tknow why, but it's just kind of funny but anyways basically an l'hospital's rule basically you know you'll, you'll arrive at a situation one day when you'retaking the limit of a function anyone×39’re going to end up with somethinglike this you×39’re going to end up with like zero over zero you know one of these situations right here you're going to find yourself and trapped in one of these things and l'hospital's rule is basically a way around it okay so basically if you end up in this situation while taking the limit of function okay I think the goal is maybe you can rewrite it as a rational function you know and we×39’ll do some examples you know maybe it×39’s in the form where there's a function divided by another function well and the limit as Goes to a just want to take the derivative of the top over the derivative of the bottom okay and Thais really the only thing you really got to keep in mind you know and now Done×39’t it only works when you have this form right here okay I mean toucans×39’t you know you can't evaluate like complicated limit you know if it is not#39’t if it doesn't you know you one né of these situations you can×39’t use it's basically it's just derivative of the top derivative at the bottom and if thatdoesn'’two, Anand you still haven'indeterminate form no problem you cause it over and over again until that indeterminate form goes away and then that will give you the limit okay now this ISN×39’t the official rule you know so but it×39’s just kind of bit it'basically what it is we×39’ll do some examples, and then we'll start to look at some math stuff okay so let's see here let me get let's just get an example going okay so here we go I go Get the limit of sine X the first things want to do is I want to look for that indeterminate form okay you know as 3X goes to 0sine X is going to go to zero and same with the bottom, so I'm going to get zero over zero situation which is good okay because that says that I can go ahead and use up at all the rule, so all got to do is just do derivative top derivative of the bottom ok so what'that that's a that's that's that×39;cosine 3x we could probably do this one without even thinking right now okay south×39’s three X goes to zero cosine goes to zero, so that is going to leave us on the top with three times one you know pretty easy example you know nothing too tough but that×39’s basically just basically what's what×39’s going to happen with something like that okay so let×39;see let's do another one lets uh Done×39’t know let's let's do this one let×39;go limit of natural log x over X minus one we pull dividing line here and let×39;go as X goes to one okay, so it's at so natural log of one you know that's that×39’s a zero and if we go one minus on ewe get zero over zero again right okays that's definitely an indeterminate form so it×39’s okay we can go ahead and use the rule so let×39’s just go...
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