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# Help with taylor expansion. watch

1. Around x-=0 to x^2

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

I get quite far but cant simplify it.. just the final step.
2. (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)
3. (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
4. (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 ...
5. (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!
6. (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.
7. (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.
8. (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
9. (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.
10. (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.
11. (Original post by shahbaz)
Yeah, I know now, be kind its only my first year lol.
no worries

(+5 reciprocated)

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