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.
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.
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 ?