
#1
Jan2014, 10:34 PM

P: 285

Hi,
I've attached a screenshot in which a solution simplifies an expression given x>>a. I have been trying to simplify and express the equation as shown, but keep failing to recognize how they reached their solution. If anyone could provide a stepbystep breakdown that would be greatly appreciated! 



#2
Jan2014, 10:58 PM

HW Helper
P: 3,436

When [itex]x>>a[/itex] then you can assume that [tex]x\pm a\to x[/tex] In other words, you just cancel the a when it's in a similar form to the above.
[tex]3x^2a^2\approx 3x^2[/tex] for example. 



#3
Jan2114, 08:54 PM

P: 285





#4
Jan2114, 10:51 PM

Sci Advisor
HW Helper
Thanks
P: 25,173

Cannot simplify 



#5
Jan2114, 11:39 PM

Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 11,530

$$\frac{1}{x(1a/x)} = \frac{1}{x}\left[1+\frac{a}{x}+\left(\frac{a}{x}\right)^2 + \left(\frac{a}{x}\right)^3 + \cdots \right].$$ If you say $$\frac{1}{xa} \rightarrow \frac{1}{x},$$ you're only taking the zerothorder approximation. The firstorder approximation would be $$\frac{1}{xa} \rightarrow \frac{1}{x}+\frac{a}{x^2}.$$ You generally want to keep enough terms to find the first nonvanishing order in some calculation. 


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