Equivalent search of functions...

John_Bilout

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Joined
Aug 19, 2005
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11
Hello...
I'm having troubles with some exercices concerning equivalents...

For example, i have to search the equivalent of

1/(1-(x)^x) - 1/(x*ln(x)).

I tried in very differents ways to solve it but each time it didn't work.
So i would like to have a solution for this kind of exercices because i have plenty to do and i don't succeed in solving it.

Thank you for an answer and sorry for the english ( i'm french indeed )
 
What do you mean by "equivalent functions"? (If you're not sure of the terminology, perhaps it might be helpful if you posted an example from your text.)

Thank you.

Eliz.
 
Well, when i say equivalent, it's like that : ln(1+x) is equivalent near 0 to x
or if u want : tanx is equivalent near 0 to x.
 
And i forgot in my subject : i shall find the equivalent when x~0.
Thank u for helping.
 
John_Bilout said:
Well, when i say equivalent, it's like that : ln(1+x) is equivalent near 0 to x or if u want : tanx is equivalent near 0 to x.
"Equivalent" to what? And how? What do you mean by "equivalent functions"?

Eliz.
 
Right, i think i didn't explain very well : for example near 0, ln(1+x)~x because when x is near 0, the 2 functions ln(1+x) and the identity function (x) have approximatively the same value.

For example if u search the limit near 0 of this expression :


Let A = ln(1+x)*sin(x)/(5*x^2) u can use equivalents :

As ln(1+x)~x and sin(x)~x u have :

A~x*x/(5x^2)
A~1/5 and u can check if u want : what is the limit of A near 0 ? u' ll find 1/5.

So now i hope u have understood what i mean and thank u for ur answer...
 
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