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Help with C1!

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Reply 40
It means (nr)=n!(nr)!r!\displaystyle \binom{n}{r} = \frac{n!}{(n-r)! r!}, so for example (42)=4!2!2!=244=6\displaystyle \binom{4}{2} = \frac{4!}{2!2!} = \frac{24}{4} = 6.
(edited 7 years ago)
Reply 41
Original post by 34908seikj
It means n "choose" r if that makes sense.
Whatever is within that matrix substitute accordingly into it.


It's read as n choose r, it doesn't mean that's what it is.

It's not a matrix.
I edited my post to clarify.
You look so cute in your new profile picture ; you have great facial structure and your glasses are very trendy . Your old pic was so bad but this one is a massive improvement. You look like such a nice person :biggrin:
Original post by Zacken
It means (nr)=n!(nr)!r!\displaystyle \binom{n}{r} = \frac{n!}{(n-r)! r!}, so for example (42)=4!2!2!=244=6\displaystyle \binom{4}{2} = \frac{4!}{2!2!} = \frac{24}{4} = 6.


so in that case (n r) = 6?

the (n r) is short for that equation with the factorial, in simple terms?
Original post by fefssdf
You look so cute in your new profile picture ; you have great facial structure and your glasses are very trendy . Your old pic was so bad but this one is a massive improvement. You look like such a nice person :biggrin:


im trying to find the right expression to share so that it gives an accurate impression of me. but I'm a bit more sarcastic online so this smiley face doesnt sometimes match with what im typing :redface: thanks anyways :hoppy:
Reply 46
No. (4 2) = 6. (n r) = n!/(r!(n-r)!)

the (n r) is short for that equation with the factorial, in simple terms?


Yes.
Original post by Zacken
No. (4 2) = 6. (n r) = n!/(r!(n-r)!)



Yes.


thankssssss another problem off my list :hoppy:
Yes, that's the binomial function, (n c) is a short way of writing it just like if I said f(x) rather than 2x+1.
You know on your calculator, there is a button called nCr and you use that when dealing with this.
It ha to do with factorials and the top number is 'n' and the bottom number is 'r'.
It's used to expand brackets in C2 (basically something like (2x+5)^10


Just an example if you want to expand (x+1)^2 you do
0C2(1^2)(x^0) + 1C2(1^1)(x^1) + 2C2(1^0)(x^2) =
= 1(1) + 2(1)(x) + 1(x^2) =
= 1+ 2x + x^2

Obviously in C2 you won't get asked this easy question and they will want the first 3/4 terms only.

Also may I suggest that you look at examsolutions videos on C1/C2, they are really helpful
Awww haha ; I like your emojis as well with the dancing bear but could you tell us what type of animal it actually is ?
I think it would be useful for you to also note that this binomial function also follows Pascal's Triangle:


As you may notice, you begin with the 3 1's at the tip, and to get a number the row below, you simply add the two above that number; eg: 2=1+1, 4=1+3, 10=4+6 as these are above them. The top row is the 0th row, and the left-most number is the 0th one.

Here's the example:


When you say something like (42)\displaystyle \binom{4}{2} You are looking at the 4th row's 2nd number from the left. As you can see, the binomial function has symmetry which is useful.

I think this can prove useful to some people who may wish to memorise the first few rows of the binomial function.

Edit: This also shows you that within (nr)\displaystyle \binom{n}{r}, rr takes any positive integer values from 0 up to nn and nothing above or below that restriction. This can be notated by 0rn0\leq r \leq n for r,nNr,n\in\mathbb{N}.
You can refer to the actual function to see what if r>nr>n, then you would be having a factorial of a negative number on the denominator which can't be done as they are undefined due to division by 0; which you should notice if you know the pattern amongst the factorials.
(edited 7 years ago)
Original post by RDKGames
I think it would be useful for you to also note that this binomial function also follows Pascal's Triangle:


As you may notice, you begin with the 3 1's at the tip, and to get a number the row below, you simply add the two above that number; eg: 2=1+1, 4=1+3, 10=4+6 as these are above them. The top row is the 0th row, and the left-most number is the 0th one.

Here's the example:


When you say something like (42)\displaystyle \binom{4}{2} You are looking at the 4th row's 2nd number from the left. As you can see, the binomial function has symmetry which is useful.

I think this can prove useful to some people who may wish to memorise the first few rows of the binomial function.

Edit: This also shows you that within (nr)\displaystyle \binom{n}{r}, rr takes any positive integer values from 0 up to nn and nothing above or below that restriction. This can be notated by 0rn0\leq r \leq n for r,nNr,n\in\mathbb{N}.
You can refer to the actual function to see what if r>nr>n, then you would be having a factorial of a negative number on the denominator which can't be done as they are undefined due to division by 0; which you should notice if you know the pattern amongst the factorials.


thank you, you've helped me answer the question ''why though'' :rofl:
Reply 53
If you want "why" then you can interpret (nr)\binom{n}{r} as the number of ways of choosing rr elements (disregarding order) from a set of nn elements.
I'm currently doing differentiation from first principles and the formula f(x+h) - f(x) / h is confusing me

say we have a curve 5x^2 - x - 1

why would the f(x+h) become 5(x+h)^2 - (x+h) ?

i dont get the substitution in this part. i get that f(x) = 5x^2 - x - 1
but how come having a ''h'' in f(x+h) make it 5(x+h)^2 - (x+h)?

from my common sense it would be 5x^2 - x - 1 + h but obviously my common sense is wrong
Reply 55
If f(x)=5x2x1 f(x)=5x^2-x-1 then for f(x+h) f(x+h) you replace all x's with (x+h). So f(x+h)=5(x+h)2(x+h)1 f(x+h)= 5(x+h)^2-(x+h)-1 .
Original post by B_9710
If f(x)=5x2x1 f(x)=5x^2-x-1 then for f(x+h) f(x+h) you replace all x's with (x+h). So f(x+h)=5(x+h)2(x+h)1 f(x+h)= 5(x+h)^2-(x+h)-1 .


Ok thats a bit clearer now in my head but i dont think they had the -1 at the end in the answer video im watching...or is my mind tricking me at the moment ?
This motivated me to do some maths. Tight now I'm on complex numbers :smile:


Posted from TSR Mobile
If you consider substituting "x" with say, 5 for f(5), then the equation would be 5(5)2 - 5 - 1. If you substitute "x" with "x + h" as the new function is f(x + h), then it becomes 5(x + h)2 - (x + h) - 1. The expression in the brackets substitutes into the variable in your original function.
(edited 7 years ago)
Isn't differentiation from first principles from FP1? Or did I miss somewhere that you'd doing FM? I don't think it's in C1.

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