![]() ![]() Limit as x approaches c truly is equal to L. We will introduce a mathematically-rigorousĪllow us to do things like prove that the Mathematically-rigorous definition of limits. Progress and start thinking about taking a lot of limits. Understanding of limits, and it really will We would say the limit of f of x as x approachesĬ is equal to L. We would kind of write that mathematically is Would denote it is we would call that the limit. That value that f of x seems to be approaching Larger than c, then our f of x is right over there. When x gets a little bitĬloser to c, our f of x is right over there. That are larger than c? Well, when x is over here,į of x is right over here. Get closer and closer to c from values of x To c from the left, from values of x less than c. Of x is getting closer and closer to some We see that our f of x seems to be- as x getsĬloser and closer to c it looks like our f Maybe really almost at c, but not quite at c, then When x gets a little bitĬloser, then our f of x is right over there. ![]() When x is a reasonableīit lower than c, f of x, for our function that we Thought about a limit is what does f of xĪpproach as x approaches c? So let's think about Why a limit might be relevant where a function is notĭefined at some point. Interesting, at least for me, or you start to understand You can find the limit asĪctually is defined, but it becomes that much more And just for the sake ofĬonceptual understanding, I'm going to say it's Looks something like that, could look like anything,īut that seems suitable. And it is written in symbols as: lim x1 x21 x1 2. The limit of (x21) (x1) as x approaches 1 is 2. We want to give the answer '2' but can't, so instead mathematicians say exactly what is going on by using the special word 'limit'. So that right overįirst quadrant, although I don't have to. When x1 we don't know the answer (it is indeterminate) But we can see that it is going to be 2. PS:I hope this helps and not confuses you more becomes (x+3) so if we put x= something very close to 2, f(x) will become something very close to 5 But if we put limit x->2 (x-2) will become something either just less than 0 or just more than 0 so we can cancel them out like now our eq. will become 0/0 and you can't just cancel 0/0. We can take limit at a place where f(x) is defined eg f(x)=x^2 an put a limit x->3 here the ans will be same as f(3)=9(ie x is approaching 9 at f(3)) so its not that useful for a defined value of f(x).īut for an function like that given in "limits by factoring" video where f(x)=(x+3)(x-2)/(x-2) func is undefined at x=2 so we will use limit to know what value does the graph gives nearby f(2). But we mostly use limits where the function is undefined (ie discontinuous) to understand what the graph would look like very close to that point. ![]()
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