Very, very indeterminate

Calculus Level 3

$\large L = \displaystyle \lim_{x\to 0^+} (\log \cot(x))^{\tan(x)}$

If the number of digits of $L$ be $a$ , find $L + a$

2 solutions

Ajinkya Shivashankar
Nov 3, 2016

Take log and write tan x as 1/cot x

$log(L)=\frac{log(log(cotx))}{cotx}$ as cotx tends to infinite

So log(L)=0 or L=1 or a=1 i.e L+a=2

Krishna Shankar
Jul 5, 2016

Graph makes it easier.So the answer to the limit is 1 and number of digits is 1 indeed , L+a = 2 .