Evaluate the limit: lim_{x to 0} left[ frac{l | vedclass

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(C) Let $L = \lim_{x 	o 0} \frac{\log |2 + x| - \log |2 - x|}{	an x}$.Since the limit is in the form $\frac{0}{0}$, we apply $L$'$H$ôpital's Rule:$L

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(C) Let $L = \lim_{x 	o 0} \frac{\log |2 + x| - \log |2 - x|}{	an x}$.Since the limit is in the form $\frac{0}{0}$, we apply $L$'$H$ôpital's Rule:$L = \lim_{x 	o 0} \frac{\frac{d}{dx}(\log |2 + x| - \log |2 - x|)}{\frac{d}{dx}(	an x)}$$L = \lim_{x 	o 0} \frac{\frac{1}{2 + x} - \frac{1}{2 - x}(-1)}{\sec^2 x}$$L = \lim_{x 	o 0} \frac{\frac{1}{2 + x} + \frac{1}{2 - x}}{\sec^2 x}$Substitute $x = 0$:$L = \frac{\frac{1}{2} + \frac{1}{2}}{\sec^2(0)} = \frac{1}{1} = 1$.

Evaluate the limit: $\lim_{x \to 0} \left[ \frac{\log |2 + x| - \log |2 - x|}{\tan x} \right]$

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