One more limit

1. Mar 23, 2008

Math_Geek

1. The problem statement, all variables and given/known data
lim as x goes to 1 from the right of 2^1/x-1=inf

2. Relevant equations

solve using delta-epsilon

3. The attempt at a solution

i am not sure how to prove an infinite limit, I have a defn that states, If for epsilon>0 there exists an M>0 such that x>M implies |f(x)-L|< epsilon. My main problem is that I am not sure how to do it, and how to get the power of two out of the way

2. Mar 23, 2008

ircdan

take the log

3. Mar 23, 2008

Math_Geek

is the definition right?

4. Mar 23, 2008

ircdan

did you mean lim x->1+ 2^(1/(1-x)) = 0?

Last edited: Mar 23, 2008
5. Mar 23, 2008

Math_Geek

no the problem says it goes to inf

6. Mar 23, 2008

ircdan

Oh it's lim x->1+ 2^(1/(x-1)), which is inf yea

The correct definition is

lim x->a+ f(x) = inf if for all M > 0 there is a d > 0 s.t. 0 < |x-1| < d and x > 1 implies |f(x)| > M