Proving Infinite Limit using Delta-Epsilon: One More Limit Homework Statement

[Math_Geek]

Homework Statement

lim as x goes to 1 from the right of 2^1/x-1=inf

Homework Equations

solve using delta-epsilon

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

 

[ircdan]

take the log

 

[Math_Geek]

is the definition right?

 

[ircdan]

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

 

[Math_Geek]

no the problem says it goes to inf

 

[ircdan]

no the problem says it goes to inf

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