Originally Posted by
CMartins I need help in calculating this limit:
lim x->e+ (logx)^(1/x-e)
This gives me an indeterminate form which is 1^inf. ( log(e)=1; 1/(e-e) = 1/0+ = inf )
I proceed to follow a process that always helped me in these indeterminate forms, which is applying the exponential:
lim x->e+ e^[log(logx)^(1/(1-e))] =
= lim x->e+ e^[(log(logx))/(x-e)]
Now, it's when I get confused:
I proceed to substitute the x for the e+, which gives me:
e^[(log(log(e))/(e-e)]
log(e) = 1; therefore log(log(e)) = log(1) = 0
e-e = 0; since it's a lateral limit form the right side, e-e=0+
Which gives me the result of e^(0/0+)
I don't know where to go from here. Is 0/0+ and indeterminate form? Did I do something wrong?