Question

Log [2-x/a] - cot(x-a)​

Answer 1

$\footnotesize\rm { L = \displaystyle\lim_{ x \longrightarrow a} \ \log \big ( 2 - \frac{x}{a} \big ) \ \cot(x-a) [ 0 \times \infty] }$ form

$\rm { = \displaystyle\lim_{ x \longrightarrow a} \frac{ \log \big ( 2 - \frac{x}{a} \big ) }{ \tan ( x-a)} \bigg [ \frac{0}{0} \bigg ] }$ form

By L' hospital rule

$\rm { = \displaystyle\lim_{ x \longrightarrow a} \frac{ \frac{1}{ \big ( 2 - \frac{x}{a} \big ) } \times \big ( \frac{-1}{a} \big )}{ \sec^{2} ( x-a)}}$

$\large\rm { = \frac{ \big ( \frac{-1}{a} \big ) }{1}}$

$\large\boxed{\rm { = \frac{-1}{a}}}$