ltx→03x+x7x-5x LHL=ltx→0- 3x+x7x-5x =ltx→0- -3x+x-7x-5x =-2-12 =16RHL=ltx→0 3x+x7x-5x =ltx→0+ 3x+x7x-5x = 42=2 LHL≠RHL Limit doesnot exist

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$\underset{x \to 0}{L t} \frac{3 |x| + x}{7 |x| - 5 x} =$

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does not exist

$\frac{3}{7}$

$\frac{3}{10}$

$\frac{3}{2}$

answer is D.

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Detailed Solution

$\begin{array}{rcl} \underset{x \to 0}{lt} \frac{3 |x| + x}{7 |x| - 5 x} \end{array}$
$\begin{array}{rcl} LHL & = & \underset{x \to 0 -}{lt} \frac{3 |x| + x}{7 |x| - 5 x} \\ = & \underset{x \to 0 -}{lt} \frac{- 3 x + x}{- 7 x - 5 x} \\ = & \frac{- 2}{- 12} = \frac{1}{6} \\ RHL & = & \underset{x \to 0}{lt} \frac{3 |x| + x}{7 |x| - 5 x} \\ = & \underset{x \to 0 +}{lt} \frac{3 x + x}{7 x - 5 x} \\ = & \frac{4}{2} = 2 \\ LHL & \neq & RHL \\ Limit doesnot exist \end{array}$