Recent content by Perplexed

Thank you for your reply, it is very helpful. Just to clear things up so that someone else looking at this doesn't get confused, in my second approximation I had f(x)= \frac{1}{\sqrt{1 - x}} rather than the f(x)= \frac{1}{\sqrt{1+ x}} that you started with: notice the "-" rather than "+" in the...

I have been looking at material properties such as thermal expansion of metals which usually involves very small coefficients. The general equation of thermal expansion is usually L_\theta = L_0 ( 1 + \alpha \theta) where L is the length and theta is the temperature change. The coefficient...

That does it! Thanks. Not quite so Perplexed.

Would you mind explaining something for me please? When I first saw x = \dfrac{1 - ay/2}{\sqrt{1-ay}} and given that a << 1, I thought I might be able to simplify it using the rule \sqrt{1-x} \rightarrow (1-x/2) and \dfrac{1}{\sqrt{1-x}} \rightarrow (1+x/2) so that it became x = \dfrac{1 -...

Wow! Thanks for that, I will need some time to absorb and understand it, but thanks for working through it for me.

I'm sure this is easy but it has got me baffled. I'm told that the binomial theorem can be used to simplify the following formula x = \dfrac{1 - ay/2}{\sqrt{1-ay}} to (approximately) x = 1 + a^2 y^2 / 8 if a << 1. Thanks for any help or pointers on this one in particular, and/or general...