Thread: Small problem

So I have this simple expression, which is part of long equation: sqrt(1-(r/R)^2)). By using r<<R1 and r<<R2 I can approximate and should end up with this expression: 1-1/2(r/R)^2.

It's one of those things I could spend weeks on and still not figure out. I have really no clue how to understand how that approximation works. Any help appreciated. Maybe it's a Taylor series thing?

Originally Posted by hellfish

So I have this simple expression, which is part of long equation: sqrt(1-(r/R)^2)). By using r<<R1 and r<<R2 I can approximate and should end up with this expression: 1-1/2(r/R)^2.

It's one of those things I could spend weeks on and still not figure out. I have really no clue how to understand how that approximation works. Any help appreciated. Maybe it's a Taylor series thing?

let ... note for small values of , as depicted in the attached graph.

yes, the 2nd degree Taylor polynomial approximation of centered at is