Find the maximum value of the expression lflo | vedclass

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(C) The range of the function $f(x, y) = 	an^{-1} x - 	an^{-1} y$ is $(-\pi, \pi)$. Therefore,the maximum value of $\lfloor 	an^{-1} x - 	an^{-1}

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(C) The range of the function $f(x, y) = 	an^{-1} x - 	an^{-1} y$ is $(-\pi, \pi)$. Therefore,the maximum value of $\lfloor 	an^{-1} x - 	an^{-1} y floor$ is $\lfloor \pi^- floor = 3$.The range of the function $g(u, v) = \sin^{-1} u - \sin^{-1} v$ is $[-\pi, \pi]$. Therefore,the minimum value of $\lfloor \sin^{-1} u - \sin^{-1} v floor$ is $\lfloor -\pi floor = -4$.To maximize the expression $\lfloor 	an^{-1} x - 	an^{-1} y floor - \lfloor \sin^{-1} u - \sin^{-1} v floor$,we take the maximum value of the first term and subtract the minimum value of the second term.Maximum value $= 3 - (-4) = 7$.

Find the maximum value of the expression $\lfloor \tan^{-1} x - \tan^{-1} y \rfloor - \lfloor \sin^{-1} u - \sin^{-1} v \rfloor$,where $\lfloor . \rfloor$ denotes the greatest integer function,and $x, y, u, v$ are independent real variables.

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