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TIFR-2019-Maths-A: 9

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Let $f:\left ( 0,\infty \right )\rightarrow \mathbb{R}$ be defined by $f\left ( x \right )=\frac{sin\left (x ^{3} \right )}{x}$ . Then $f$ is

  1. bounded and uniformly continuous
  2. bounded but not uniformly continuous
  3. not bounded but uniformly continuous
  4. not bounded and not uniformly continuous
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