x → ∞ lim 2 2 x 1 = ?
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To make it abundantly obvious, perform a change of variables x → y 1 . Then the limit becomes lim y → 0 2 2 y . In this case we can now directly substitute because f ( y ) = 2 2 y is defined at y = 0 : lim y → 0 2 2 y = 2 2 0 = 1 .
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As x approaches Infinity, 1/x approaches 0, so 22^(1/x) approaches 1. Here '^' is power notation.