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$\lim\limits_{x\to 1}(\log_33x)^{\log_x3}$ is

$(a)\;1\qquad(b)\;e\qquad(c)\;e^2\qquad(d)\;None\;of\;these$

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$\lim\limits_{x\to 1}(\log_33x)^{\large\log_x3}=\lim\limits_{x\to 1}(\log_33+\log_3x)^{\large\log _x3}$
$\Rightarrow \lim\limits_{x\to 1}(1+\log_3x)^{\Large\frac{1}{\log_3x}}$
$\Rightarrow e$
Hence (b) is the correct answer.
answered Dec 23, 2013 by sreemathi.v
 

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