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C4 Binomial Expansion

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    I have 2 questions to this topic:

    1. What do they mean by finding the range of values where x is valid

    2. and how approximations work

    In the picture for example, apart from the fact that I don't know about approximations, where do they get the 1/10 from?

    I would have thought to sub root10 in f(x)

    Click image for larger version. 

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    1. I think that means domain (all possible x values). For example, the |x|<1 after the function.

    2. Think of a binomial expansion with increasing powers of x. What if |x|<1? As an arbitrary variable 'k' tends to infinity, the value of x^k tends to 0. Therefore, the sum of the first 'k' terms of the binomial expansion (1+x)^n approaches (as long as k<n) (1+x)^n.

    This is especially apparent if x=10^-k. With each 'new' term of the binomial expansion, you're increasing your accuracy by 'k' decimal points because you're getting 10^k times closer to the exact value with each 'new' term.

    As for where they got the 1/10 from, it's given in (a) ^^;


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