<p>
</p>
<p>In lay terms,
lim (approaching 1)^(approaching ∞) = e,
provided “approachings” proceed at the right paces respectively - as in
lim (1+1/n)^n = e.
n->∞</p>
<p>So
lim x^(1/(x-1)) = e
x->1</p>
<p>===================
Here’s the proof.
lim (1+1/n)^n = e
n->∞</p>
<p>Substitution t=1/n yields
lim (1+t)^(1/t) = e
t->0</p>
<p>Substitution x=1+t yields
lim x^(1/(x-1)) = e</p>
<h1>x->1</h1>
<p>Or you could just pull out your old trustworthy TI-89 and feed it
limit(x^(1/(x-1)),x,1). It’s still e.
lmsao</p>
<p>===================
I.dont.know, it sure looks like homework to me. ;)</p>