How is Taylor expansion used in physics?

[spaghetti3451]

I wasn't sure where to put this, so I put this here!

In the photo, you see there's written 'Taylor expanding for small delta-r₂, we find' ...

I really don't get the two steps in the next line.

Any help would be greatly appreciated.

 

[rbj]

he skips some steps. consider $(r_2-r_1)$ as a single quantity and $\Delta r$ as another quantity. ignore the $(\Delta r)^2$ term in the expansion as being super small. then use:$$(1 + \Delta)^p \approx 1 + p \Delta$$

for small $|\Delta|$.

so multiple approximations are going on here.

 

[spaghetti3451]

I see! But i still don't get the step after that. Any hints?

 

[rbj]

I see! But i still don't get the step after that. Any hints?

what? the $\Delta d$ thing?

i have a suggestion, do you know how to use TeX? try it out and spell out the equations right here. a jpg of a projected image is easy for you, but hard for me. since you're the person seeking help, it might behoove you to not make it unnecessarily difficult for whoever helps you.

but, after that approximation, it's all just algebra.

 

[spaghetti3451]

I see how it all works out, now! It's quite simple, really! But, anyway, thanks for trying to make a dumbass like me understand such a difficult concept.