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Lim X → ∞ Sin X X Equals

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प्रश्न

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

विकल्प

  •  0 

  •  ∞ 

  •  1

  •  does not exist 

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उत्तर

(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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अध्याय 29: Limits - Exercise 29.13 [पृष्ठ ७८]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 29 Limits
Exercise 29.13 | Q 8 | पृष्ठ ७८

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