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Lim X → ∞ Sin X X Equals - Mathematics

MCQ

\[\lim_{x \to \infty} \frac{\sin x}{x}\] equals 

Options

  •  0 

  •  ∞ 

  •  1

  •  does not exist 

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Solution

(a) 0

\[\lim_{x \to \infty} \frac{\sin x}{x}\]
\[Let x = \frac{1}{y}\]
\[ x \to \infty \]
\[ \therefore y \to 0\]
\[ = \lim_{y \to 0} \frac{\sin \frac{1}{y}}{\frac{1}{y}}\]
\[ = \lim_{y \to 0} y \sin \frac{1}{y}\]
\[ = \lim_{y \to 0} y \times \lim_{y \to 0} \sin \frac{1}{y}\]
\[ = 0 \times \lim_{y \to 0} \sin \frac{1}{y}\]
\[ = 0\] 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Q 8 | Page 78
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