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Hi,

On a bit of work i've got to do, theres a question mainly based on binomial expansion and the last part of the question i am not sure what to do.

Here is the question:

(a) Find the binomial expansion of (1+x)^(1/3) up to the term in x^2

(b) Show that (8+3x)^(1/3) ≈ 2 + 1/4 x -1/32 x^2 for small values of x

(c) Hence show that ∛9 ≈ 599/288

For part (a) i got 1 + 1/3 x - 1/9 x^2 and for part (b) i got the answer that it required but i haven't got a clue how to do (c)

Any help would be appreciated

Thanks

On a bit of work i've got to do, theres a question mainly based on binomial expansion and the last part of the question i am not sure what to do.

Here is the question:

(a) Find the binomial expansion of (1+x)^(1/3) up to the term in x^2

(b) Show that (8+3x)^(1/3) ≈ 2 + 1/4 x -1/32 x^2 for small values of x

(c) Hence show that ∛9 ≈ 599/288

For part (a) i got 1 + 1/3 x - 1/9 x^2 and for part (b) i got the answer that it required but i haven't got a clue how to do (c)

Any help would be appreciated

Thanks

Put x=1/3 in (b)

Let 8 3x = 9

Solve for x x = 1/3

Sub back into binomial expansion

2 + (1/4)(1/3)x (1/32)(1/3)^2

=599/288

Solve for x x = 1/3

Sub back into binomial expansion

2 + (1/4)(1/3)x (1/32)(1/3)^2

=599/288

Original post by kaprice ricot

Let 8 3x = 9

Solve for x x = 1/3

Sub back into binomial expansion

2 + (1/4)(1/3)x (1/32)(1/3)^2

=599/288

Solve for x x = 1/3

Sub back into binomial expansion

2 + (1/4)(1/3)x (1/32)(1/3)^2

=599/288

You're replying to a thread that is 10 years old! I think the OP is sorted by now

- What topic are you on at school in Further maths yr 12?
- Epq or core maths as plus 1
- A levels/gcse resits
- How many exams and assignments does the LPC have?
- Trampoline Exercises That Will Challenge Your Body
- Help I am concerned about my grades!
- High intensity therapy
- Low GCSE grades, what to do?
- what a-levels should i take and what job should study for?
- A level maths UMS marks!!!
- university of york field trips? biological sciences
- what laptop/Mac/ computer is recommended for doing a BA animation?
- Does Oxford accept bad AS grades?
- GCSE resit that is not core
- UCL BASc Arts and Sciences 2023 offer holders
- What happens if you fail your KCL retake exams?
- How hard is this A Level choice?
- Can I study PPE at a top university? (With a grade 5 in gcse foundation maths)
- A-level chemistry. Draw a labelled diagram to show the formation of the π-bond.
- Which A-levels?

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can someone please explain what principle domain is and why the answer is a not c?Maths

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