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Hi everyone!
I'm abit stuck on the question below. Can anyone help?
1. Evaluate √(1.05) correct to 5 significant firgures.
hint: use a series for (1+x)^(1/2)
Thank you
Kind Regards,
Enita
We have the binomial expansion:
Now if we set x = 0.05 the we will have an expansion for
Substitute this value into the series to give:
No point in going further as we are beyond five significant figures accuracy so add these to give:
to 5 s.f.Offline
Glad that we only need to evaluate Taylor Polynomials to the 2nd derivative.
Taylor Polynomials to the 2nd derivative:
f(x[sub]0[/sub]+h)=f(x[sub]0[/sub])+f'(x[sub]0[/sub])h+(1/2)f"(x[sub]0[/sub])h²
In this case, f(x)=x)^(1/2)
x[sub]0[/sub]=1, h=0.05, so you can work out f'(1) and f"(1) alone.
Indeed, there is a special formula of (1+x)^(1/2), but I forgot. You may look it up your calculus book.
Last edited by George,Y (2007-01-31 02:35:37)
X'(y-Xβ)=0
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Thank you for you quick response!
how did you know to set x to equal 0.05 ?
Kind regards
Enita
We need to find:
And I have a series which gives me the value of:
where x can be any number whose modulus is less than 1.Well, I notice that
which looks identical to my formula if only the 'x' in that formula were replaced by 0.05. And it's okay to use the formula because the modulus of 0.05 < 1.
Mitch.
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Thank you!
Nicely explained.