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    How do I show that if x is small the expression root(1+x)/(1-x) is approximated by 1 +x +1/2xsquared
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    (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.
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    What's a binomial
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    (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.
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    But then I get 1+x+1/4xsquared and not 1/2x squares?
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    (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?
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    (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.
    Oh is that like C2 Binomial Expansion?
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    (Original post by Jademorgan1)
    But then I get 1+x+1/4xsquared and not 1/2x squares?
    What are you multiplying together?
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    (Original post by M4cc4n4)
    Oh is that like C2 Binomial Expansion?
    That's exactly what it is, yes.
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    (Original post by NotNotBatman)
    What are you multiplying together?
    I am multiplying( 1+1/2x)(1+1/2x)
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    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
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    (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.
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    (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!
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