Alevel maths
How do I show that if x is small the expression root(1+x)/(1-x) is approximated by 1 +x +1/2xsquared
Original post by Jademorgan1
How do I show that if x is small the expression root(1+x)/(1-x) is approximated by 1 +x +1/2xsquared
By expanding the binomial up to the term in x^2.
Original post by M4cc4n4
What's a binomial
A polynomial consisting of the sum of two terms.
in this case (1-x) and (1+x) are binomials, which can be approximately expanded when raised to a power using the binomial theorem, provided x is small.
But then I get 1+x+1/4xsquared and not 1/2x squares?
Original post by NotNotBatman
By expanding the binomial up to the term in x^2.
But then I get 1+x+1/4xsquared and not 1/2x squares?
Original post by NotNotBatman
A polynomial consisting of the sum of two terms.
in this case (1-x) and (1+x) are binomials, which can be approximately expanded when raised to a power using the binomial theorem, provided x is small.
in this case (1-x) and (1+x) are binomials, which can be approximately expanded when raised to a power using the binomial theorem, provided x is small.
Oh is that like C2 Binomial Expansion?
Original post by Jademorgan1
But then I get 1+x+1/4xsquared and not 1/2x squares?
What are you multiplying together?
Original post by M4cc4n4
Oh is that like C2 Binomial Expansion?
That's exactly what it is, yes.
Original post by NotNotBatman
What are you multiplying together?
I am multiplying( 1+1/2x)(1+1/2x)
As I have converted the root(1+x)/(1-x) to two binomials of (1+x) to the half and 1-x to the half and then expanded them each separately to get the first two terms of each and then multiplied these together
Original post by Jademorgan1
I am multiplying( 1+1/2x)(1+1/2x)
expand each binomial up to the term in x^2 and then multiply out and ignore terms of higher powers.
Original post by NotNotBatman
expand each binomial up to the term in x^2 and then multiply out and ignore terms of higher powers.
Thankyou so much!
Quick Reply
Related discussions
- Computer science alevel
- Science subjects + a humanity for A Level?
- 16-18 Education
- Bad predicted grades in year 12
- CHange alevel choices
- Medicine HELP
- A-level decision help - Medicine at oxbridge
- Economics degree/apprenticeship
- Question about lse accounting and finance
- Can I study economics/computer science at uni without maths a level?
- FM as an A-Level
- Maths for economics at Nottingham university
- A level options
- Can i go into quant finance if im not going to a "top 5" university?
- How much Maths in Biology and Psychology A Level?
- Biology and chemistry
- A level physics without maths
- A level choices
- Should I take core maths?
- Does anyone actually care about A-Level Computer Science?
Latest
Trending
Last reply 2 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 2 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
