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TIFR-2011-Maths-A-6

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The function $f_{n}(x)= n \sin (x/n)$

  1. Does not converge for any $x$ as $n \rightarrow \infty$
  2. Converges to the constant function $1$ as $n \rightarrow \infty$
  3. Converges to the function $x$ as $n \rightarrow \infty$
  4. Does not converge for all $x$ as $n \rightarrow \infty$
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