# A2 C4 maths help please explain question

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#1
On question 2 why do we use binomial expansion?
On question 1b why are the limits flipped when you take out a quarter?
the solutions are below
0
3 years ago
#2
The limits are flipped because they get rid of the minus. When evaluating an integral you can flip the limits by taking the negative of the integral, essentially multiplying the whole thing by -1. They use binomial cuz thats essentially what the question is asking you to do. "Suffienctly small" means it has a limit, just like in a binomial expansion, eg:modx<2/3. so thats a hint to use binomial esoansion.
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#3
The limits are flipped because they get rid of the minus. When evaluating an integral you can flip the limits by taking the negative of the integral, essentially multiplying the whole thing by -1. They use binomial cuz thats essentially what the question is asking you to do. "Suffienctly small" means it has a limit, just like in a binomial expansion, eg:modx<2/3. so thats a hint to use binomial esoansion.
i see so binomial expansion is not only to expand without having to do a tonne of work its also to find the smallest possible value or a value to a limit! i get it thanks.
0
3 years ago
#4
(Original post by BubbleBabby)
i see so binomial expansion is not only to expand without having to do a tonne of work its also to find the smallest possible value or a value to a limit! i get it thanks.
It’s to find a suitable estimate when x is small.

I get the feeling you don’t really understand C4 binomial expansion properly
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#5
It’s to find a suitable estimate when x is small.

I get the feeling you don’t really understand C4 binomial expansion properly
i don't think i do i thought binomial expansion was to avoid pascals triangle but when i have to do it for things when the expansion does not the binomial expansion i don't understand that. Why is it when you expand that fraction manually and via binomial expansion you get 2 different answers surly you should get the same answer?
0
3 years ago
#6
(Original post by BubbleBabby)
i don't think i do i thought binomial expansion was to avoid pascals triangle but when i have to do it for things when the expansion does not the binomial expansion i don't understand that. Why is it when you expand that fraction manually and via binomial expansion you get 2 different answers surly you should get the same answer?
Pascal’s triangle coefficients work only for positive integers as the series is finite (there is a fixed number of terms)

But when you use a fraction or negative number as your index (basically all of C4 expansions) you only expand it manually. It also is an infinite sequence because, if you think about it, when you subtract 1 from a fraction or negative, you never get to 0, therefore the numerator of the coefficient never gets to 0 for the series to stop. You’ll therefore stop the series at a reasonable place (usually at x^3 or x^4). You might want to look at exam solutions, a short vid that explains everything better
0
#7
Pascal’s triangle coefficients work only for positive integers as the series is finite (there is a fixed number of terms)

But when you use a fraction or negative number as your index (basically all of C4 expansions) you only expand it manually. It also is an infinite sequence because, if you think about it, when you subtract 1 from a fraction or negative, you never get to 0, therefore the numerator of the coefficient never gets to 0 for the series to stop. You’ll therefore stop the series at a reasonable place (usually at x^3 or x^4). You might want to look at exam solutions, a short vid that explains everything better
Thanks
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