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

Instructions and Help about When Form 8815 Limitations

Okay and this example or a couple examples we're going to talk about limits at infinity either positive infinity or negative infinity and the idea is the same in a regular-- limit in this case with the notation means is you're putting in you know values of x in this case they get larger and larger and larger so maybe I'll put a hundred into this formula get a number out I'll put excuse me a thousand into this formula get a number out I'll put a million into the formula get a number out a billion a trillion a gajillion and you just keep going and going and going and the idea is you know if the numbers you're getting out are getting closer and closer to something again that's what we say the limit is and these problems limits at infinity I like a little bit better only in the sense that they're a little more straightforward they're the basic ones are a bit more mechanical and again just like anything in math there's definitely variations on this theme but when you have a rational function and again that's a polynomial over a polynomial you always look at the highest power of X in the denominator so in this case my highest power of X is X cubed and what we're going to do is we divide every single term and the problem by x cubed so I'll get the limit x goes to infinity I'll take three x squared divide that by X cubed I'm going to take five X divide that by X cubed I'll take four divide that by X cubed I'll have X cubed over X cubed and then I'll have seven x over x cubed okay so the next thing here which is we just simply simplify this down a little bit so 3x squared over X cubed I'll have one X left over in the denominator 5x over X cubed I'll get 5 over x squared well there's not much to do with the 4 over X cubed term so we'll just leave that alone X cubed over X cubed is 1 and we have 7x over X cubed so that will give me 7 over x squared ok at this point we've kind of done our simplification and the idea is now okay so X is getting bigger and bigger and bigger well let's think about 3 over X what's going to happen to that well 3 over 10 3 over a hundred 3 over a thousand 3 over 10,000 3 over a million a billion you know if you put those numbers into a calculator you'll see that they're all getting closer and closer to the number 0 so that's what happens to this piece as X goes to infinity we'll get 0 for this same thing 5 over a number that's getting bigger and bigger if we square it this whole term is going to go to 0 also 4 over X cubed is also going to become 0 well one stays one same thing with our 7 over x squared that's going to go off to 0 so what are we left with well we're left with 0 on top one on the bottom and it says our limit in this case is going to equal 0 let's do one more of these let's look at say the limit as X goes to negative infinity of X to the fourth plus X over 5x to the 8th let's not make it 5 X to the 8th let's make it 5 X to the 3rd +7 so again I'm picking on X to the 3rd same idea though I pick out the highest power of X in the denominator well again I've got an X to the 3rd that's my highest power of X in the denominator and I'm going to divide everything by that so I've got X approaching negative infinity I'll have X to the 4th divided by X to the 3rd I've got X divided by X to the 3rd I've got 5 X to the 3rd divided by X to the 3rd and then I have 7 divided by X to the 3rd so let's keep simplifying we have the limit as X goes to negative infinity well X to the fourth divided by X that leaves me with 1/x x over X to the third that's 1 over x squared 5 X to the third over X to the 3rd is 5 and then there's nothing to do with the 7 over X to the 3rd just like before okay so well as X is going to negative infinity we'll think about this term in a second but notice 1 over x squared just like before this is going to go off to 0 again whether I take a negative number or a positive number I'm going to get a big number in the denominator well 1 over a big number whether it's positive or negative will go to 0 the same thing with 7 over X to the third that's going to go to 0 and what are we really left with well if these terms are going to 0 as X goes to negative infinity well X will go to negative infinity so we're left with negative infinity divided by 5 well that's still equivalent to negative infinity if you take a big negative number and divide it by 5 it's still a big negative number and that would be your solution so in this case you could say that this limit does not exist sometimes people will we say that to me it's a little clearer to say that it going off to negative infinity it gives you a little more insight into what's happening so some useful little tricks for these limit problems are as follows let me cover them up here the first case and these work if