Hey... This question is beyond me...

find lim as x -> 0

f(x) = 1 / ((x+1)^(1/x)) - 1/x

any help would be greatly appreciated.

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- November 9th 2009, 07:33 PMLandyachlimits involving x-root functions
Hey... This question is beyond me...

find lim as x -> 0

f(x) = 1 / ((x+1)^(1/x)) - 1/x

any help would be greatly appreciated. - November 9th 2009, 08:01 PMBacterius

You want :

Therefore, you want :

Let's not forget that (depending on which side you come from)

Consider if you are approaching on the positive side :

Ugly, eh ?

Which by absorption (I'm not sure about the last part) :

The other possibility (approaching on the negative side) seems quite harder (since you get some weird results) but since I'm not really sure about what I've just done, I won't go on. - November 9th 2009, 08:05 PMProve It
- November 9th 2009, 08:07 PMBacterius
What do you mean ? My maths teacher told us the inverse of x could have two different limits in 0 depending if you approach 0 from the negative side (the limit is -infinity) or the positive side (the limit is +infinity).

Was he wrong or was I just doing something else when he said this ?

EDIT : now that I think about it I remember he said something about 0, maybe he said ? - November 9th 2009, 08:29 PMProve It
- November 9th 2009, 08:37 PMLandyach
- November 9th 2009, 08:48 PMBacterius
Yes you are right, it is basically the same thing on the other side, my mistake.