help

[cara.mel]

Second monster:
def mysin(x, n):
   if (n == 0):
   {
      return x
   }
   else:
   {
      return + mysin(x, n - 1)
   }

Thank you for translating it neobeo. although I don't understand what it does still. Does x get a number as well as n? Why are there 2 numbers in the ()

edit: and how does it look in normal maths

[Ahmad]

[Ahmad]

x gets a number as well, right. The function accepts two arguments, that's why the there are two labels in the argument paranthesis. That happens when you want to pass over more than one piece of information to a function.

[cara.mel]

1. why/how does that work
2. is it in radian or degree
3. does it keep going forever or does it stop at 90 or so

I will try and work through it, but first:


So if I had:
dim x, y as integer
x=5
y=1
function addnumber(x,y)
x + y
end function

it would return 6?

and if it was
dim x, y as integer
x=5
y=1
function addnumber(x,y)
x^2 + y
end function

it would return 26?
(I dont remember how functions work and where the number goes but anyway.)

[AppleXY]

HEY, that's the taylor's series.

http://en.wikipedia.org/wiki/Taylor%27s_series

[cara.mel]

http://en.wikipedia.org/wiki/Taylor%27s_series#List_of_Taylor_series_of_some_common_functions

how did they know to change it for each one. how did they get it from the first one way at the top of the article. it doesnt make sense.

how does a series work. i have been told i should know that from year 11 so im dumb.

[Ahmad]

dim x, y as integer
x=5
y=1
function addnumber(x,y)
x^2 + y
end function

it would return 26?

Looks good, you might have to write return x^2 + y though, depending on the programming language. (The details are irrelevant really, since it's language specific).

It's in radians and has a radius of convergence of infinity, this means you can plug in any value! However, that would only be true if you used the whole infinite number of terms. If you cut off this series at some point, you'd get more accurate results by plugging in values closer to zero, this is because this taylor series is said to be "centered" at 0. So if you put in x = 10^(10^10), you probably wouldn't get very accurate results with a small finite number of terms.

[Ahmad]

http://en.wikipedia.org/wiki/Taylor%27s_series#List_of_Taylor_series_of_some_common_functions

how did they know to change it for each one. how did they get it from the first one way at the top of the article. it doesnt make sense.

how does a series work. i have been told i should know that from year 11 so im dumb.

As far as I know Taylor Series do not crop up in high school.

Here's one method of finding the result for .

Suppose that for some numbers :



By plugging in x = 0, you get

Now differentiate both sides of the equation and set x = 0 again, getting:





By repeating this process you can calculate all the coefficients, the pattern will soon emerge!

[cara.mel]

but aidan said i should know of a series in general and i dont and he wouldnt explain it to me =(

not this type, this is in like week 10 or 11 or so of mth1030.

why are there subscripts, in like a1, I dont follow that.

[Neobeo]

In VB(script) it would look like

dim x, y as integer
x=5
y=1
function addnumber(x,y)
addnumber = x^2 + y
end function

Here, the "addnumber = x^2 + y" is really assigning the value "x^2 + y" to the function. The difference between this and "return" is that "return" immediately terminates the function. In VB(script) the only way to terminate a function or routine is by "end function" or "exit function".

[Ahmad]

Subscripts are used to name different constants that we want to calculate. I could've used a, b, c, d etc, but it is much more convenient and systematic to use subscripts to distinguish between them.

Aidan was probably referring to sequences and series which are taught at a rudimentary level in further maths. This would be sequences of numbers, which is basically a function that has the domain of the natural numbers. For example consider f(n) = 3n + 2, with domain the natural numbers. Then you could write the sequences of numbers defined by f by calculating f(1), f(2), ... (5, 8, 11, ...).

You will probably study sequences and series in a more rigorous manner when you take calculus and learn about convergence, and methods of finding whether a series converges/diverges.

[cara.mel]

so a0=a, a1=b, a2=c etc?
*me tries to understand now I get that*

Edit: wait, how does it work for x=1 then o_O, because how do I find a b c

f(n) = 3n + 2 - how does that work. why does it keep going. what is the point of it then because it would just be infinity when you add them together. (the ... mean it keeps going right?)

[Ahmad]

If you add together the terms of a sequence, you get a series. You're right, in this case the series would diverge, but that isn't always the case. This occurs for example with f(n) = (1/2)^n.

And yes, ... means it keeps going.

[cara.mel]

So in those does n go from 1-> infinity, and you keep subbing in new numbers?

What is a sequence and a series

[midas_touch]

http://en.wikipedia.org/wiki/Taylor%27s_series#List_of_Taylor_series_of_some_common_functions

how did they know to change it for each one. how did they get it from the first one way at the top of the article. it doesnt make sense.

how does a series work. i have been told i should know that from year 11 so im dumb.

The first time I was taught series was last year at uni, so dont worry. Simply, a series is an infinite sum of terms. In the case of the Taylor series, this gives a polynomial representation of a particular function, since each term in the series is a polynomial.