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If F ( X ) = X Sin 1 X , X ≠ 0 , Then the Value of the Function at X = 0, So that the Function is Continuous at X = 0, Is(A) 0 (B) −1 (C) 1 (D) Indeterminate - Mathematics

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Question

If  \[f\left( x \right) = x \sin\frac{1}{x}, x \neq 0,\]then the value of the function at = 0, so that the function is continuous at x = 0, is

 

Options

  • 0

  • −1

  • 1

  • indeterminate

MCQ
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Solution

Given: 

\[f\left( x \right) = x \sin\frac{1}{x}, x \neq 0\]

Here,

\[\lim_{x \to 0} x \sin \left( \frac{1}{x} \right) = \lim_{x \to 0} x \lim_{x \to 0} \sin\left( \frac{1}{x} \right) = 0 \times \lim_{x \to 0} \sin\left( \frac{1}{x} \right) = 0\]

If f(x) is continuous at x = 0, then

\[\lim_{x \to 0} f\left( x \right) = f\left( 0 \right)\]
\[\Rightarrow f\left( 0 \right) = 0\]
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Chapter 9: Continuity - Exercise 9.4 [Page 46]

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RD Sharma Mathematics [English] Class 12
Chapter 9 Continuity
Exercise 9.4 | Q 35 | Page 46

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