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# C4, binomial expanision

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1. I am doing the paper June 2013(R)
Stuck on 4(b) where it says: using your expansion to estimate an approximate value of (7100)^1/3
For my expansion I got 2-(3/4)x-(9/32)x^2-(45/256)x^3
The Original function is (8-9x)^1/3
If anyone could help it would be good as I don't understand atand what the mark scheme is doing
2. (Original post by Dnaap)
I am doing the paper June 2013(R)
Stuck on 4(b) where it says: using your expansion to estimate an approximate value of (7100)^1/3
For my expansion I got 2-(3/4)x-(9/32)x^2-(45/256)x^3
The Original function is (8-9x)^1/3
If anyone could help it would be good as I don't understand atand what the mark scheme is doing
This question:
Spoiler:
Show
~ Realised I misread one part of the question which made my post wrong ~
3. If you make x=1/10 what do you get inside the cube root?

you get 71/10 so we have .
Now you need to multiply this by some number to get .
4. (Original post by Dnaap)
I am doing the paper June 2013(R)
Stuck on 4(b) where it says: using your expansion to estimate an approximate value of (7100)^1/3
For my expansion I got 2-(3/4)x-(9/32)x^2-(45/256)x^3
The Original function is (8-9x)^1/3
If anyone could help it would be good as I don't understand atand what the mark scheme is doing
so:

.

Then, if you let you get

So plugging into your expansion gets you an approximation for

But

So once you put in into your expansion, you approximate - you need to multiply it by to get .
5. (Original post by B_9710)
If you make x=1/10 what do you get inside the cube root?

you get 71/10 so we have .
Now you need to multiply this by some number to get .
Why x=1/10 though? How do you know to put 1/10 in
6. (Original post by Zacken)
so:

.

Then, if you let you get

So plugging into your expansion gets you an approximation for

But

So once you put in into your expansion, you approximate - you need to multiply it by to get .
Thanks very thorough I'm just not sure why you chose to put 1/10 in
7. (Original post by Zacken)
so:

.

Then, if you let you get

So plugging into your expansion gets you an approximation for

But

So once you put in into your expansion, you approximate - you need to multiply it by to get .
Never mind I got it reading over your working. Thank you a lot!
8. (Original post by Dnaap)
Never mind I got it reading over your working. Thank you a lot!
9. (Original post by Zacken)
so:

.

Then, if you let you get

So plugging into your expansion gets you an approximation for

But

So once you put in into your expansion, you approximate - you need to multiply it by to get .
How come I get different answers when I put both the LHS and RHS into my calculator? According to what you wrote they should be equal right?
.
10. (Original post by Glavien)
How come I get different answers when I put both the LHS and RHS into my calculator? According to what you wrote they should be equal right?
.
Sorry, yes. The first line of my answer is a fail. (the rest is fine) It should be .
11. (Original post by Zacken)
Sorry, yes. The first line of my answer is a fail. (the rest is fine) It should be .
Ahh thanks, that must mean the first line of the mark scheme is wrong too.
12. (Original post by Glavien)
Ahh thanks, that must mean the first line of the mark scheme is wrong too.
Sounds like it.

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