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Binomial expansion and approximation question

Hey! Could some one point me in the right direction for part b. ii. ?
Also if you spot any mistakes in my working please let me know : )
Thanks!
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Reply 1
Avatar for Zacken
Zacken
22
Original post by Matt Howard
Hey! Could some one point me in the right direction for part b. ii. ?
Also if you spot any mistakes in my working please let me know : )
Thanks!


(a) All correct.

(b) (i) All correct except for the last line. You're not allowed to willy-nilly multiply things like that.

Your answer as 13−2x81+82187x2\frac{1}{3} - \frac{2x}{81} + \frac{8}{2187} x^2 is the correct and final (simplified) answer.

(ii) 27+6x=2827 + 6x = 28 means that (27+6x)−1/3=(28)−1/3=1281/3(27 + 6x)^{-1/3} = \left(28\right)^{-1/3} = \frac{1}{28^{1/3}}

So just solve 27+6x=2827 +6x = 28 then plug this value of xx into your expansion. But you're still off by a factor of something so you'll need to multiply your answer by that.
(edited 8 years ago)
Reply 2
Avatar for KaylaB
KaylaB
20
Original post by Matt Howard
Hey! Could some one point me in the right direction for part b. ii. ?
Also if you spot any mistakes in my working please let me know : )
Thanks!


If you've found the expansion for (27+6x)^(-1/3) which is that same as 1/(27+6x)^(1/3)
And you're trying to find 2/28^(1/3)

You could try making 28 = 27+6x and find a suitable value for x

By substituting that value of x in to your expansion, this would give you 1/28^(1/3) so what would you need to do to get it to 2/28^(1/3)?
Reply 3
Avatar for KaylaB
KaylaB
20
Original post by Zacken
(a) All correct.

(b) (i) All correct except for the last line. You're not allowed to willy-nilly multiply things like that.

Your answer as 13−2x81+82187x2\frac{1}{3} - \frac{2x}{81} + \frac{8}{2187} x^2 is the correct and final (simplified) answer.

(ii) 27+6x=28827 + 6x = \frac{28}{8} means that (27+6x)−1/3=(288)−1/3=281/3(27 + 6x)^{-1/3} = \left(\frac{28}{8}\right)^{-1/3} = \frac{2}{8^{1/3}}

So just solve 27+6x=28827 +6x = \frac{28}{8} then plug this value of xx into your expansion.


Why is it 28/8 instead of 28?

Spoiler

Reply 4
Avatar for Zacken
Zacken
22
Original post by KaylaB
Why is it 28/8 instead of 28?

Spoiler



Doesn't count because the last bit of what I sad was wrong! :tongue:

It should be 2828, I was rushing out for dinner when I posted what I did. Thanks. I'll correct it!
Reply 5
Avatar for KaylaB
KaylaB
20
Original post by Zacken
Doesn't count because the last bit of what I sad was wrong! :tongue:

It should be 2828, I was rushing out for dinner when I posted what I did. Thanks. I'll correct it!


This is what happens when you rush things :colone:
Reply 6
Avatar for Zacken
Zacken
22
Original post by KaylaB
This is what happens when you rush things :colone:


:colondollar: Oh well, t'was a team effort, I pointed out a mistake in (i) you gave the correct approach to (ii). :biggrin:

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