How Do Taylor Series Help Solve Water Wave Velocity Problems?

[beatboxbo]

Homework Statement

A water wave has length L moves with velocity V across body of water with depth d, then v^2=gL/2pi•tanh(2pi•d/L)
A) if water is deep, show that v^2~(gL/2pi)^1/2
B) if shallow use maclairin series for tanh to show v~(gd)^1/2

Homework Equations

Up above

3. The Attempt at a Solution

Have no idea where to start, just looking for some tips and I'm assuming I need the tanh series for both parts, this has been the hardest calculus for me

 

[diazona]

Well, first things first: define "deep" and "shallow". In each case it means that one of your variables is much less, or much greater, than another. Figure out which quantity is less/more than which other one in each case, and that should tell you what variable or combination of variables to use for your series expansion.

Also, you can look up the series expansion for tanh(x) on Wikipedia, among other places.