The kernels $nx^n$ concentrate near x = 1, with total mass $\int_0^1nx^ndx=n/(n+1)\to1$. For any fixed δ > 0, the mass on [0,1−δ] tends to zero exponentially, while eˣ is uniformly close to e on the remaining short interval when δ is small. Continuity therefore gives the integral limit e = 2.7182818, rounding to 2.718.
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