Question

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

विकल्प

•  0 

•  ∞ 

•  1

•  does not exist 

Answer 1

(a) 0

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