Hi,

I said that I started to learn limits. Since often I write about the things I just learn I will start this series today with the very basic. (The start is actually so easy you wont even think that it is precalculus or something)

Basicly the context for limits are functions. I have personally never learned functions on

their own and I do plan to do that but I do not think it is so important right now. You just

have to have this idea that when you have function you will give it some input and it will give out some output (kind of black box).

It is important to say that one input corresponds only to one output. You have already probably seen some graphs so it is good to say that you can plot a function.

The thing with outputs and inputs can be nicely illustrated on one thing: imagine a class of kids and that you measure them.

Carl – 157 cm

Ann – 152 cm

Caroline – 160 cm

… and so on

Now you will plot them on graph next to each other. In big enough class you would probably have more kids with same height.

On the left we have three example kids from one class. As is written, Ann has 152 centimeters, Susan 152 too but Jacob has 149,155 and 161 centimeters. Such class would not make a great function! The interesting thing is of course that to one height (152 cm) you can match more people (Ann and Susan), this makes sense. But you can not match one person to more heights! This is the way function works. You could just change names and heights for x and y and you would be there[1]. So if you graph some function it will never be vertical and basicly no two values will ever be above each other, when you on the other hand plot equation you can easily get graph where there are two points above each other:

So… what role do limits play here? As you probably already heard, limit tolds us what value will function give us when we give it input really close to some number. If you have function like

f(x)=x^2 (f(x) is the way functions are noted, you could use other symbols)

You can ask for limit of x approaching to any real number and you would get the same as if you would calculate x to the power of 2. The real usage of limits comes when there is point where you can not get some nice value and also I think that it is defined by limits if function is continous (without jumps) or not.

I will slowly continue in the next post 😉

Dragallur

PS: some of my readers mathematicians (or anybody), if there please point out any mistakes, I am just learning this so it would be great to know my mistakes!

[1] To make it even clearer I made this extra picture:

At some point you need to put this stuff out in book form …sell it on Amazon or something ….I love the way you simplify things …put your own slant on it ….this stuff would be great for kids …OR big kids like myself who just didn’t ‘get’ maths and the sciences at school:)

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Thanks! Always appreciate your words Fijay!

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