Binomial series expansion- approximations help c4

Hi

I'm struggling on question 2B part ii. . I have managed to do part I but I have no idea on how to use that answer for part ii.

I feel I am struggling generally regarding approximations also.

Thanks for your help

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Reply 1

TeeEm

19

Original post by the_googly

Hi

I'm struggling on question 2B part ii. . I have managed to do part I but I have no idea on how to use that answer for part ii.

I feel I am struggling generally regarding approximations also.

Thanks for your help

Posted from TSR Mobile

you need to use your expansion with a suitable value of x

Reply 2

the_googly

OP

7

Original post by TeeEm

you need to use your expansion with a suitable value of x

It tells me to use 0.1....?

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Reply 3

TeeEm

19

Original post by the_googly

It tells me to use 0.1....?

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sure

cube root of (1 - 01) =
cube root of (0.9) =
cube root of (9/10) =
cube root of (900/1000)=

cube root of (900) / cube root of (1000)

cube root of (900) / 10

Does this help?

Reply 4

username1434402

3

Original post by the_googly

Hi

I'm struggling on question 2B part ii. . I have managed to do part I but I have no idea on how to use that answer for part ii.

I feel I am struggling generally regarding approximations also.

Thanks for your help

Posted from TSR Mobile

(900)^(1/3)=(1000^(1/3))(1-0.1)^(1/3)

Reply 5

the_googly

OP

7

Original post by ahf

(900)^(1/3)=(1000^(1/3))(1-0.1)^(1/3)

Hi sorry for the late reply. Your method gives the correct answer however the question says I have to substitute 0.1 in the expansion to find the answer?

Reply 6

the_googly

OP

7

Original post by TeeEm

sure

cube root of (1 - 01) =
cube root of (0.9) =
cube root of (9/10) =
cube root of (900/1000)=

cube root of (900) / cube root of (1000)

cube root of (900) / 10

Does this help?

Hi sorry for the late reply, your method gives the same answer for part (i)?

Reply 7

username1434402

3

Original post by the_googly

Hi sorry for the late reply. Your method gives the correct answer however the question says I have to substitute 0.1 in the expansion to find the answer?

yes so you substitue x=0.1 into (1-x)^1/3

Reply 8

username1434402

3

and you know what 1000^1/3 is

Reply 9

the_googly

OP

7

Original post by ahf

and you know what 1000^1/3 is

Sorry I am struggling... So how would that help?

Reply 10

davros

16

Original post by the_googly

Sorry I am struggling... So how would that help?

You want the cube root of 900. 900 = 0.9 x 1000 so the cube root of 900 is the cube root of 0.9 x the cube root of 1000.

You know what the cube root of 1000 is. Your binomial expansion gives you an approximation for the cube root of 0.9. Therefore you can estimate the cube root of 900 :smile:

Binomial series expansion- approximations help c4

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