Towering Limit!

Calculus Level 3

$\large \lim_{x\rightarrow 0^+} f(x)$

Let $f(x)$ be the exponent tower with finite number of $x$ 's. Which of the given scenarios is true about the limit above?

Bonus: What about infinite number of $x$ 's? Would the limit exist?

\displaystyle\lim_{x\to0^+}f(x)

can either be

0

1

, depending on the number of

x

\displaystyle\lim_{x\to 0^+} f(x) = 0

for any number of

x

\displaystyle\lim_{x\to 0^+} f(x) = 1

for any number of

x

1 solution

Sabhrant Sachan
Feb 21, 2017

$\displaystyle \lim_{x \to 0^{+} } f(x) = \begin{cases} 1 & n\text{ mod 2} = 0 \\ 0 & n\text{ mod 2 } = 1 \end{cases}$

Where ' $n$ ' is the no. of $x$ in the tower

Any extra explanation possible? I am curious how it all works.

Peter van der Linden - 4 years, 3 months ago

That is the pattern for the problem. Can you try proving it by induction? :)

It's interesting to see you approach the bonus problem!

Michael Huang - 4 years, 3 months ago