# Thread: limitation problem

1. hello:
may anybody help me with this in my practicing book.

lim(ln(1+x)/x)=lim[(1/x)ln(1+x)] 1)
=lim(ln(1+x)^(1/x)) 2)
=ln(lim(1+x)^(1/x)) 3)
=lne=1 4)
(x->0)

i don't understand how to derive 3) from 2) based on which principal or theorem.

any comment is appreciated.

2.

3. hello:
may anybody help me with this:
here is my problem:
calculate:lim((1-4x)^((1-x)/x)) (x->0) 1)

here is my process of solving it:
1)=lim(1+(x/-(1/4)))^(-4/x)*(1+x/(-1/4))^(5/x-1)
=e*lim(1+x/(-1/4))^(5/x-1)
=e*lim(1+x/(-1/4))^lim(5/x-1)
=e*1^(infinite big number)
=e

obvious even i myself know it is wrong.but how can i solve it

any comment is appreciated.

4. limitation problem:
hello:
may anyone give me a hint on this
i have to solve this based on two theorem of e:

lim(1+x)^(1/x)=e (x->0)
and lim(1+(1/x))^x=e (x->infinite big positive or small negative)

the problem:
the value of lim((1+x)/(1-x))^(1/x) (x->0)

5. Posts merged.

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