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TIFR-2019-Maths-A: 11

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Let $f$ be a continuous function on $\left [ 0,1 \right ]$. Then the limit $\underset{n\rightarrow \infty }{lim}\int ^{1}_{0}nx^{n} f\left ( x \right )dx$ is equal to 

  1. $f(0)$
  2. $f(1)$
  3. $\underset{x\in\left [ 0,1 \right ]}{sup} f\left ( x\right )$
  4. The limit need not exist
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