square root using Taylor series

smslca

As I am new to Taylor series, and im little confused, and in an urgent to expansion of sqrt
I want Taylor expansion for

sqrt{[(100*c)+21-p]^2-[8400*c]}

where "p" is constant. and "c" is variable.
and c>=1,

I know I should do it by myself. But I need it in urgent.can anyone please expand it for me.

Polynomial

smslca wrote: »

sqrt{[(100*c)+21-p]^2-[8400*c]}

Just to check the expression you want to expand:

[LATEX]
\sqrt{[100c+21-p]^2-8400c}
[/LATEX]

Is that it?

MathsManiac

...and you need to say what the centre of the expansion is. If c is the variable, as you said, you need to say "Taylor series about c=..." Otherwise the question can't be answered.

gerardduff

MathsManiac wrote: »

...and you need to say what the centre of the expansion is. If c is the variable, as you said, you need to say "Taylor series about c=..." Otherwise the question can't be answered.

Let's assume you want to expand about c=a, a>1

Now, you should have a look at the following and apply it to your problem,
after that we can maybe talk about the expansion in more detail.

The series expansion of,

[LATEX]
\sqrt{1-x}
[/LATEX]

about x=a, is

[LATEX]
1-\frac{1}{2}(x-a)+\left(\frac{(\frac{1}{2})(\frac{-1}{2})}{2!}\right)(x-a)^2+...
[/LATEX]

This seems to be the most sensible way to tackle this for a beginner. Of course, I'm kinda hoping you've done a binomial expansion before and are happy with factorising surds or whatever you call square root type things these days. If you can do this you might be ready to do Taylor series. The above is just a special case of that, and you can shape you expression to look like it....maybe?