Math, asked by sanket138, 5 months ago

Log [2-x/a] - cot(x-a)​

Answers

Answered by Anonymous
41

\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}}}

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