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$\underset{x \to 0}{\lim} x \sin \left( \frac{1}{x} \right)$ equals

  1. $-1$
  2. $0$
  3. $1$
  4. Does not exist
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1 Answer

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Sin(x) can range from [-1, 1], so whatever be the value of x, sin(1/x) belongs to this range i.e a fiinite value

Now, x * sin(1/x) = x * finite value, where x->0

so it should be 0 only

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