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cool man, series expansion, thanks

but t/5 is not << 1

phi we don't know about that, so I just assumed it

it would be if the premise is that t is small to begin with, in that case t/5 would be smaller

but it is that assumption

thanks unless you have a belligerent way to do it phi

did you plug your answer back into the original equation?

phi you're right it won't work, we'll have to include higher order terms

I just didn't think of doing the expansion in the first place

rather couldn't

I've got to roll, but thanks for the help guys

Do you mean no computers and no wolfram?
A problem like this without calculators would take a while!

It's not clear what the constraints are on how to do this problem. But generally, you would solve it using numerical techniques. such as http://en.wikipedia.org/wiki/Newton's_method
see attached pdf for result