Correct answer: (B) gₙ converges uniformly but fₙ does not.
Explanation
Both sequences converge pointwise to zero on (0,1). But $\sup_{0<x<1}x^n=1$, so fₙ does not converge uniformly. For gₙ the maximum occurs at $x=n/(n+1)$ and equals $(n/(n+1))^n/(n+1)\leq1/(n+1)\to0$. Thus gₙ converges uniformly, giving B.
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