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  • Among  <img alt="\lim _{x \rightarrow 0} \sec ^{-1}\left(\frac{x}{\sin x}\right)\,\,.... (1)" src="/latex-image/?%5Cli

Among  \lim _{x \rightarrow 0} \sec ^{-1}\left(\frac{x}{\sin x}\right)\,\,.... (1)  and   \lim _{x \rightarrow 0} \sec ^{-1}\left(\frac{\sin x}{x}\right) \,\,....(2) 

 

Option: 1

(1) exists, (2) does not exist


Option: 2

(1) does not exist, (2) exists


Option: 3

both (1) and (2) exist


Option: 4

neither (1) nor (2) exists


Answers (1)

best_answer

\frac{x}{\sin x}   is more than 1 in the neighbourhood of ' 0 '. Hence \lim _{x \rightarrow 0} \sec ^{-1}\left(\frac{x}{\sin x}\right) exists while  \frac{\sin x}{x} is less than 1 in the neighbourhood of ' 0 '. Hence   \lim _{x \rightarrow 0} \sec ^{-1}\left(\frac{\sin x}{x}\right) does not exist.

Posted by

Suraj Bhandari

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