How do I prove using an $\epsilon - \delta$ proof that $\lim_{x\rightarrow \frac{1}{e}}(e^{x^{x^x}})<2$?

Not a homework question. Just wanting to refresh my epsilon delta proofs, and came up with this - struggled for an hour, no idea where to start.

• You might note that $e>2$ so $1/e < 1/2$. The function is strictly increasing for $x>0$, so evaluating at $x=1/2$ might be easier than evaluating at $x=1/e.$ – B. Goddard Mar 15 at 13:15
• Yes it stops at $e^{x^x}$. – Daniel S Mar 15 at 13:16