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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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Evaluate the following limits: $ \lim\limits_{x \to 0} \large\frac{ \sin \: ax}{bx}$

$\begin{array}{1 1} \frac{a}{b} \\ \frac{b}{a} \\ \frac{-a}{b} \\ \frac{-a^2}{b}\end{array} $

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1 Answer

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At $ x = 0 $ the value of the given function is $ \large\frac{0}{0}.$
Using, $ \large\frac{ \sin \: ax}{bx}$$ =\large\frac{ \sin \: ax}{ax} $$ \times \large\frac{ax}{bx}$$ = \large\frac{\sin\;ax}{ax}$$\times\large\frac{a}{b}$
$ \Rightarrow \lim\limits_{x \to 0} \large\frac{ \sin \: ax}{bx}$$ = \lim\limits_{x \to 0} $$\bigg( \large\frac{ \sin \: ax}{ax} \bigg)$$ \times \bigg( \large\frac{a}{b} \bigg) $
$ = \large\frac{a}{b}$$ \lim\limits_{ax \to 0} \bigg( \large\frac{ \sin\: ax}{ax} \bigg) $ $ \quad \quad \quad [ x \to 0 \Rightarrow ax \to 0]$
$ \lim\limits_{y \to 0} \large\frac{\sin \: y}{y}$$=1$
$ = \large\frac{a}{b}$
answered Apr 4, 2014 by thanvigandhi_1
edited May 16, 2014 by balaji.thirumalai
 

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