લક્ષ અને વિકલન — ગણિત ધોરણ 11 સાયન્સ — Question

$\lim_{x \rightarrow 1^-}\frac{\sqrt{\pi}-\sqrt{2sin^{-1}x}}{{\sqrt{1-x}}}$ $sin^{-1}=T$ લેતા

$\lim_{T \rightarrow \frac{\pi}{2}}^-\frac{\sqrt{\pi}-\sqrt{2T}}{\sqrt{1-sinT}}$ $\therefore x=sinT$

$\lim_{T \rightarrow \frac{\pi}{2}}^- \frac{\pi-2T}{(\sqrt{\pi}+(\sqrt{2T})\sqrt{1-sinT}}$

$\lim_{^T \rightarrow \frac{\pi}{2}}^- \frac{2(\frac{\pi}{2}-T)}{(2\sqrt{\pi})\sqrt{1-cos(\frac{\pi}{2}-T)}}$

$\lim_{h \rightarrow 0^{+}}\frac{h}{\sqrt{\pi}\sqrt{1-cos \ h}}$

$=\sqrt{\frac{2}{\pi}}$