Binomial Theorem - small values of x and approximate values

[Bucky]

"Show that for small values of x, the function (1+x)^(-1/2) may be approximated by

1-(1/2)x+(3/8)x^2

Hence obtain the approximate value of 1/root(1.01) to 4 decimals."


im totally clueless. the example we have isn't well explained at all. can someone even just start me off?


(incidentally what happened to the flex pluggin? i went to find it for the maths bits but can't find it)

 

[Tide]

Just replace x with 0.01 in your binomial expansion and you will have the desired approximation.

 

[Bucky]

what about the initial 'show that' bit?

 

[AKG]

Do you know the binomial theorem?

 

[Bucky]

(a+b)^n = a^n +na^(n-1)b + (n(n-1))/2! (etc) ...that one?

 

[Integral]

That's the one!

Now you have 1.01 , think of it as a+b where a=1 and b=.01.

Now, plug that into the binomial expansion, look at the magnitude of each monomial as you add them, continue until the terms are below your desired error.

 

[Bucky]

ok thanks for your help guys..just one more question..

where did you get 1.01/0.01 from?

 

[HallsofIvy]

ok thanks for your help guys..just one more question..
where did you get 1.01/0.01 from?

?? I don't see any reference to 1.01/0.01 in any of the previous responses!