mathop {lim }limits_{x to frac{pi^+}{2}} e^{[ | vedclass

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(D) We need to evaluate $\mathop {\lim }\limits_{x 	o \frac{\pi^+}{2}} e^{[\cot x]}$.As $x 	o \frac{\pi^+}{2}$,$x$ is slightly greater than $\frac{\

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$\frac{1}{e}$

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(D) We need to evaluate $\mathop {\lim }\limits_{x 	o \frac{\pi^+}{2}} e^{[\cot x]}$.As $x 	o \frac{\pi^+}{2}$,$x$ is slightly greater than $\frac{\pi}{2}$.In this interval,$\cot x$ is negative and approaches $0$ from the negative side (i.e.,$\cot x \in (-1, 0)$ for $x$ just above $\frac{\pi}{2}$).Therefore,the value of $[\cot x]$ is $-1$.Substituting this into the expression,we get $e^{-1} = \frac{1}{e}$.

$\mathop {\lim }\limits_{x \to \frac{\pi^+}{2}} e^{[\cot x]}$ is equal to :-
(where $[.]$ is the greatest integer function)

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$\mathop {\lim }\limits_{x \to \frac{\pi^+}{2}} e^{[\cot x]}$ is equal to :-(where $[.]$ is the greatest integer function)