How to Find the Limit of a Factorial Function

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Finding the limit of a factorial function in mathematics depends on two very specific things. Find the limit of a factorial function with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: Principles of Math
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to find the limit of a factorial function. Well, it really depends on two things when it comes to finding the limit of a factorial function. One, how the function is setup and two, what value is the independent variable approaching. So, for example, if you have the limit as n approaches infinity of n factorial, the idea is here you have to look at what it is approaching and how the function is setup. So, in this particular case, you have the situation where it's just going to be infinity. Now, if you have the limit as n approaches infinity of let's just say n minus one factorial over n factorial, because this function is larger, this limit ends up being zero. But, if, if you notice I've used the infinity both times, but it doesn't have to be infinity all the time. So, if you have limit as n approaches let's just say five of, let's just use something a little bit different; n minus two factorial over n minus one factorial, what this allows you to do here is plug in five into both places for n and you'll have as a result five minus two is three, so it'll be three factorial over five minus one is four factorial. And what that allows you to do is expand the factorial but at the end of the day, you'll have three times two times one over four times three times two times one. The three's, two's and one's cancel, so you're left with one fourth. So, in order to find the limit of a factorial function, you really have to determine what value of independent variables approaching and how you setup the factorials. So, I'm Jimmy Chang, and these are a few examples of how to find the limit of a factorial function.

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