Video instructions and help with filling out and completing Where Form 8815 Limitations

Instructions and Help about Where Form 8815 Limitations

Hi guys I'm Nancy and I'm going to show you how to find the limit out of value at a finite value limits are kind of a mess so I made a couple videos and here are some links to my other videos if you just want an introduction to the limits what do they mean check out the introduction video if you are looking for how to find the limit at infinity check out the limits at infinity video but this is how to find the limit out of value at a finite value so let's look at the types I'm going to cover okay these are the first four of seven ways to find the limit at a value of finite value they are the four main ways most common strategies if you already see the kind you're wondering about the kind of problem you're working on you can skip ahead you can use the links in the video just give directly to that part or you can check the description to find the exact time to skip to so let's look at them the first is to plug in if you can if you can't and I'll show you why you might not be able to try factoring if possible if not see if you can get a common denominator that means if you have something that looks like a fraction within a fraction a complex rational expression you might be able to get a common denominator if not see if you can expand open up parentheses expand simplify and then find the limit these four cases cover most of the kind of limit problems at finite values that you would get 90% of them but there are a few oddball miscellaneous misfit cases that come up so let's look at those okay these are the three miscellaneous oddball cases if you're looking for one of these I lied they're not actually in this video but you can use the links in this video to jump to that video where I explain these or look in the description for the video link basically if you have a square root and a fraction in the numerator or something like sine x over X or absolute value you'll need these strategies but forget about this for now let's look at the four most common strategies okay with these limit problems the first thing you should always try is to plug in the value plug in 4 for X everywhere X appears and see if you get a value for the limit okay so you got an actual number for the limit a finite value 5/7 is a finite unique number that is your limit the limit is equal to 5/7 and you're done but if you ever get a 0 in the bottom in the denominator or the form zero over zero which is indeterminate you have not found the limit you're not done you'll need another way another technique before I show you another technique here are some other common types of limits you can find just by plugging in these are all other limits you can find just by plugging in any polynomial you can plug in to square root of something that ends up being a square root of a positive number or square root of zero something to a power or limit of a constant a number is just that number just that constant those are all great but usually final limit is not this simple you might see this one set of 20 times usually you'll have to use another way so let me show you the next way of finding a limit okay so new problem but still the first thing you should try to find the limit is to plug in and see if you get a finite number finite value all right so you've plugged in and you did not get a finite number like 2 or and you got not only a zero in the denominator which is problematic but zero over zero the indeterminate form if you get zero in the denominator or zero over zero that is not your limit so caution warning that is not your limit you are not done it actually is assigned to you that you need to try something else to find your limit number limit value and the next best thing to try is factoring especially if your function expression has polynomials in it so this one is begging for you to try factoring it there's a difference of squares in the bottom there's a quadratic on top so you want to try to factor it this is great because after factoring we were able to plug in and get an actual number finite number 2/3 as the limit value the limit is equal to 2/3 why did this work the point of factoring was that it got rid of these problem terms X minus 3 over X minus 3 those terms that were creating the 0 over 0 form now that they're gone now that they dropped out and they've disappeared you are able to plug in and really just get the actual number that the limit is equal to well what happens if you factor in terms cancel and then you try to plug in at the end and you still get 0 in the denominator or worse 0 over 0 what then okay look at this one what if you factored cancel terms you plug in again at the end and you still get zero in the denominator which is undefined this means that your function is increasing without limit shooting off to infinity or negative infinity it's limitless and you can write DNA for the limit does not exist the limit does not exist and if you couldn't remember that you can be a state champion like the North Shore mathletes let me show you some other