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STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
Question
$\mathop {\lim }\limits_{x \to \infty } \frac{{\sin x}}{x} = $
✓

Answer

b
(b) $\mathop {\lim }\limits_{x \to \infty } \,\,\frac{{\sin x}}{x},$ let $x = \frac{1}{y}$ or $y = \frac{1}{x},$

so that $x \to \infty \,\, \Rightarrow \,y \to 0$

$\therefore \,\mathop {\lim }\limits_{x \to \infty } \,\left( {\frac{{\sin x}}{x}} \right) = \mathop {\lim }\limits_{y \to 0} \,\left( {y.\sin \frac{1}{y}} \right)$ 

$= \mathop {\lim }\limits_{y \to 0} \,y \times \mathop {\lim }\limits_{y \to 0} \,\sin \frac{1}{y} = 0 \times ... = 0$

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