lim _{x rightarrow 1}(1-x) tan left(frac{pi}{ | vedclass

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(B) Let $h = 1-x$. As $x ightarrow 1$,$h ightarrow 0$,so $x = 1-h$. Substituting this into the limit: $\lim _{h ightarrow 0} h 	an \left(\frac{

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$\frac{2}{\pi}$

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(B) Let $h = 1-x$. As $x ightarrow 1$,$h ightarrow 0$,so $x = 1-h$. Substituting this into the limit: $\lim _{h ightarrow 0} h 	an \left(\frac{\pi}{2}(1-h)ight) = \lim _{h ightarrow 0} h 	an \left(\frac{\pi}{2} - \frac{\pi h}{2}ight)$ Since $	an(\frac{\pi}{2} - 	heta) = \cot(	heta)$,we have: $\lim _{h ightarrow 0} h \cot \left(\frac{\pi h}{2}ight) = \lim _{h ightarrow 0} h \frac{1}{	an \left(\frac{\pi h}{2}ight)}$ Multiply and divide by $\frac{\pi}{2}$: $\lim _{h ightarrow 0} \frac{h \cdot \frac{\pi}{2}}{	an \left(\frac{\pi h}{2}ight)} \cdot \frac{2}{\pi} = 1 \cdot \frac{2}{\pi} = \frac{2}{\pi}$.

$\lim _{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right) = $

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