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Re: Approximation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116452] Re: Approximation
  • From: Albert Retey <awnl at gmx-topmail.de>
  • Date: Wed, 16 Feb 2011 04:33:31 -0500 (EST)
  • References: <ijdoc6$fco$1@smc.vnet.net>

Hi,

> Is there a way to tell Mathematica to simplify and approximate an
> expression assuming things such as "R is a lot smaller than G"/ R<<G ?
> If not so, how would you approach the problem?

You can tell Mathematica to do what you would probably implicitly do in
such a situation: rewrite to use R/G and G, expand in R/G and discard
powers of R/G that you consider small enough. You should look at
functions Series and Limit. Here is an example as a starting point:

Limit[(R + G + Exp[R + G])/(Tan[R/G] + Cos[R/G]) /. R -> d*G, d -> 0]

or if you want to keep higher orders:

Series[(R+G+Exp[R+G])/(Tan[R/G]+Cos[R/G]) /. R -> d*G, {d, 0, 2}]

hth,

albert


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