# Dirty Limits

Calculus Level 4

$\lim _{ x\rightarrow \infty }{ \frac { \ln { \left( x+\ln { \left( x+\ln { \left( { x }^{ \frac { 1 }{ x } } \right) } \right) } \right) } }{ \log _{ 10 }{ \left( { x }^{ 2 } \right) } } }$

This expression can be expressed as $\frac { A }{ B } \left( \ln { \left( C \right) } +\ln { \left( D \right) } \right)$ for co-prime positive integers $$A$$ and $$B$$, and prime numbers $$C$$ and $$D$$.

Find $A+B+C+D$

×