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    Around x-=0 to x^2

    (sin(x)/x)^1/2

    I get quite far but cant simplify it.. just the final step.
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    (Original post by shahbaz)
    Around x-=0 to x^2

    (sin(x)/x)^1/2

    I get quite far but cant simplify it.. just the final step.
    please post what you have done so far
    (my method is through standard expansions and binomial)
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    (Original post by TeeEm)
    please post what you have done so far
    (my method is through standard expansions and binomial)
    Firstly I used the expansion sinx = x-(x^3)/3!)+.....
    then I divided by x to give 1-(x^2)/3!
    Then I square rooted it thats as far as i can get
    I know the method is correct but the final solution was 1-x^2/12
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    (Original post by shahbaz)
    Firstly I used the expansion sinx = x-(x^3)/3!)+.....
    then I divided by x to give 1-(x^2)/3!

    Then I square rooted it thats as far as i can get
    I know the method is correct but the final solution was 1-x^2/12

    I agree with the blue

    I do not quite understand the red bit ...
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    (Original post by shahbaz)
    Firstly I used the expansion sinx = x-(x^3)/3!)+.....
    then I divided by x to give 1-(x^2)/3!
    Then I square rooted it thats as far as i can get
    I know the method is correct but the final solution was 1-x^2/12
    Binomial theorem:

    (1-A)^(1/2) = 1 - A/2 + O(A^2).

    Apply with A= x^2/3!
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    (Original post by TeeEm)
    I agree with the blue

    I do not quite understand the red bit ...
    You have to square root the entire thing to get it into the form the question wants.
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    (Original post by DFranklin)
    Binomial theorem:

    (1-A)^(1/2) = 1 - A/2 + O(A^2).

    Apply with A= x^2/3!
    Thanks will try it now.
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    (Original post by shahbaz)
    You have to square root the entire thing to get it into the form the question wants.
    I hope you do not mean what I suspect you mean

    After that it is just the first 2 terms of a binomial expansion to 1/2
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    (Original post by DFranklin)
    Binomial theorem:

    (1-A)^(1/2) = 1 - A/2 + O(A^2).

    Apply with A= x^2/3!
    it worked! I'm pretty bad at spotting things like that. Thanks again.
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    (Original post by TeeEm)
    I hope you do not mean what I suspect you mean

    After that it is just the first 2 terms of a binomial expansion to 1/2
    Yeah, I know now, be kind its only my first year lol.
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    (Original post by shahbaz)
    Yeah, I know now, be kind its only my first year lol.
    no worries

    (+5 reciprocated)
 
 
 
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