JEE MAIN - Mathematics (2003 - No. 6)
If $$\mathop {\lim }\limits_{x \to 0} {{\log \left( {3 + x} \right) - \log \left( {3 - x} \right)} \over x}$$ = k, the value of k is
$$ - {2 \over 3}$$
0
$$ - {1 \over 3}$$
$${2 \over 3}$$
Explanation
$$\mathop {\lim }\limits_{x \to 0} {{\log \left( {3 + x} \right) - \log \left( {3 - x} \right)} \over x} = K$$
(by $$L'$$ Hospital rule)
$$\mathop {\lim }\limits_{x \to 0} {{{1 \over {3 + x}} - {{ - 1} \over {3 - x}}} \over 1} = K$$
$$\therefore$$ $${2 \over 3} = K$$
(by $$L'$$ Hospital rule)
$$\mathop {\lim }\limits_{x \to 0} {{{1 \over {3 + x}} - {{ - 1} \over {3 - x}}} \over 1} = K$$
$$\therefore$$ $${2 \over 3} = K$$
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