Nesting the Limits

Calculus Level 2

Evaluate:

limx(1+1(limx(1+1x)x)x)(limx(1+1x)x)x\left\lfloor \lim _{ x\rightarrow \infty }{ { \left( 1+\frac { 1 }{ { \left( \lim _{ x\rightarrow \infty }{ { \left( 1+\frac { 1 }{ x } \right) }^{ x } } \right) }^{ x } } \right) }^{ { \left( \lim _{ x\rightarrow \infty }{ { \left( 1+\frac { 1 }{ x } \right) }^{ x } } \right) }^{ x } } } \right\rfloor

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